The Three Bees was launched in 1813. This was her first and only voyage bringing convicts to New South Wales.
Captain John Wallis was formerly Master of a slave ship taking negroes from Africa to the West Indies  He was also Master of the Fanny in 1816, the Isabella in 1822 and the Isabella in 1823.
The prisoners were convicted in counties throughout Ireland. - Antrim, Armagh, Carlow, Clare, Cork, Dublin, Donegal, Down, Drogheda, Fermanagh, Galway, Kings, Kildare, Kilkenny, Leitrim, Limerick, Londonderry, Longford, Lough, Mayo, Meath, Monaghan, Queens, Roscommon, Sligo, Tipperary, Tyrone, Waterford, Westmeath, Wexford and Wicklow. Among them were many who gave their occupation as labourer. There were also carpenters, butchers, shoemakers, millers, seamen, coopers, weavers, brickmakers, cabinetmakers, quarrymen, coach drivers, tailors, clerks, a publican, watchmaker, gun locksmith, whitesmith and some who were still school boys.
In later years convict indents included the crimes committed by the prisoners however in 1814 this wasn't done and the muster taken on the arrival of the Three Bees doesn't reveal their crimes however newspaper articles of some of the trials are included below and reveal that embezzlement, forgery, highway robbery and of administering oaths were among the crimes
From The National Archives of Ireland web site: -
Before the convict depot was opened in Cork in 1817, there were several scandals relating to those brought from Dublin in sloops or brigs to await embarkation. Because of delays, transportees sometimes had to wait on board these vessels for extended periods in appalling conditions. In 1815, Governor Macquarie complained of the high mortality rate on the Three Bees and the Catherine. The Inspector General of Prisons, Foster Archer, attributed the high rate to the fact that the convicts had to remain in dock at Dublin for six weeks awaiting suitable winds. They received neither clothing nor bedding, which were considered an unnecessary expense due to the shortness of the journey to Cork. Because only a few were allowed on deck at once, they spent most of the time in irons in the hold in very unhealthy conditions. The journey itself was made in two days, but the sloop was again detained in Cork harbour before the convicts were removed to the ship. Archer insisted that in this case it was the long detention in port which probably caused the high mortality. To support his case, he told of returned convicts who had informed him that the period spent in the harbour was more distressing than the voyage and that they underwent more suffering and sickness in the passage from Dublin to Cork than in that from Cork to Botany Bay. 
Surgeon William Redfern remarked on the circumstances of the Three Bees.....
The Convicts from the New Prison, Dublin joined those from the Northern jails, who had embarked two days before on board the Atlas hired Brig, on the 28th August 1813. The weather was sultry, and as they were exceedingly crowded in a close hold, the nights were truly suffocating. During their stay here one of the prisoners died, whose fatal termination, it was said, was accelerated, if not solely occasioned by the foulness of the place necessarily attendant on crowding so many together. They sailed from the Canal Docks, Dublin the 20th September and anchored in the Cove of Cork on the night of the 22nd. Next day they were examined by Doctor Harding inspecting Physician, and were removed on board the Three Bees as fast as they could be conveniently cleaned and dressed. This service was completed on the 2nd October. The Cork and Southern convicts with those of the Atlas completed their number two hundred and nineteen.
The military guard consisted of a detachment of the 46th regiment under charge of Lieutenant Thomas Miller, Lieutenant Hans Morrison, Ensigns Hamilton, Joseph Wilson and Ensign John Skelton and 43 non-commissioned officers and privates.
There was a great deal of animosity between Captain Wallis and the Military Guard of the 46th regiment on this voyage. Trouble began while the ship still lay at Cork Harbour on 12th September 1813 when the Military Officers invited some friends on board to dine. Tempers ran high for most of the voyage after this. There were charges of neglect of duty, revenge, drunkenness and inhumanity and the resulting enquiry provides some interesting details of the daily life of Officers and soldiers of the Guard on the voyage to Australia.
The Three Bees and the Catherine were to sail from Cork for Falmouth on the first fair wind, there to join the convoy for South America, however the voyage was delayed somewhat when a tremendous gale from the south-east accompanied with heavy rain blew up on the night of the 19th October. The Morning Post reported that the rain and wind continued the entire night and into the following day. They sailed from Cork on 27th and the Cornwall Gazette reported that they had finally anchored at Falmouth by 30th October
The weather, during the time they were at Falmouth was exceedingly cold and the prisoners suffered severely. They were, while in harbour, supplied with fresh beef; their rations were uniformly and justly served out.
While at Falmouth the convicts were presented with Bibles by the British and Foreign Bible Society. They expressed their gratitude in a letter which the surgeon of the Three Bees later presented to the society.........
From the Surgeon of the Three Bees, on a Voyage with Convicts from Cork to Port Jackson, New South Wales.
Falmouth, Nov. 25, 1813.
THIS morning I was presented with the accompanying letter, and a written request that I would forward it to the British and Foreign Bible Society.
It may be proper for me to observe, that, when I first presented the Convicts with the Holy Scriptures, many of them conceived they were furnished by Government in, the same way as their clothing and other necessaries. I then felt it my duty to inform them to whom they were indebted for the Bibles and Testaments with which they were supplied; and having established a circulating library among them, I added thereto the Report of the British and Foreign Bible Society.
Two months have now elapsed, and the inclosed voluntary effusion of gratitude is a part of the consequences. As soon as the matter was proposed (by a Roman Catholic who had never perused the Holy Scriptures before he came on board this ship) they all flocked with gratitude and anxiety to subscribe their names; and I have good reason to suppose that not a few of them acted from principle in so doing.
I do not despair of having almost every Convict able to read the Bible before we arrive at Port Jackson; and it affords me heartfelt satisfaction, that I can present a Bible to every individual on board who is capable of reading it. Your grateful and obliged servant, Mr. Joseph Tarn. T. A.
Letter referred to in the above.
To the Right Hon. Lord Teignmouth, President; the Vice Presidents, Treasurer, Secretaries, Committee, and Friends of the British and Foreign Bible Society of London. Lords and Gentlemen,
We, the Convicts on board the ship Three Bees, venture to approach your venerable Society. We acknowledge, with grateful hearts, the receipt (at the instance of our humane and respected Surgeon) of your valuable books; and humbly beg of you to accept our unfeigned thanks. Your gift (appropriate to our situation) gives us a new train for our ideas; a new object to our hopes: convincing of the necessity of seeking the kingdom of God, it assures us, we, 'in no wise, are cast out.' Formerly, to the wealthy and the literati alone, the Word of God was accessible; the fountain of salvation was polluted; ignorance poisoned the source, or debased the margin.
Your Society, like the sun, arose, and pure light was dispensed equally on all; but half the world was not its object, the universe is at once enlightened - prejudice no longer seals the book; and poverty, in your days, is not an obstacle in the way of spiritual knowledge. We humbly beg, through the medium of your Society, to convey our grateful acknowledgments to the Edinburgh, Dublin, and Cork, Bible Societies, and to the worthy individuals who have contributed to the same laudable cause by supplying us with the Holy Scriptures.
But for your Societies we should take with us, to a rude country, a store of ignorance and barbarity, while we bear the name of Christians. You gave to our solitude The Book of Books, and we have no longer dreary, immured thoughts. We see that God is with us; you have put his candle in our hands; it shineth on my head, and by his light I go through darkness. Yours is an epochal brighter than any in history: there we see the red mark of vengeance - the black track of war: or if religion was the pretence, a sect was upheld - or a particular form was sometimes propagated by the point of the sword. You propagate the Spirit of the Lord with his own book. We take it with us to a country where the natives have not yet felt the first shame that ever assailed mankind - the shame of nakedness. Let us leave our gratitude here; let our names reach you as marks of our humble veneration and sincere thanks. May the western light, which shines over the world, increase in splendour, and extend over the whole earth. May it guide and direct us all. * Lords and Gentlemen, We are your truly humble and very grateful servants, - (Signed by 169 persons.)
The Three Bees sailed from Falmouth 8th December 1813.
It was the height of the Napoleonic wars when the Three Bees and Catherine departed Falmouth and they were to sail in convoy and under the protection of the armed frigates Niger and Tagus. They parted company from the Niger and the Tagus about a month later when those vessel entered into a battle with the French frigate Ceres. Captain Rainier of the Niger later wrote of the encounter -
The Niger, in company with the Tagus frigate, Captain Pipon, on 6th January near Cape de Verde, had fallen in with the Ceres French frigate, of 44 guns and 324 men, commanded by Baron de Bougainville. The Ceres was one month from Brest on her first cruise. She was manoeuvred in a masterly style during a chase of 238 miles, when the Tagus, being to windward, opened fire, which was briskly returned; but the Enemy's main top-mast being shot away, rendered her escape impossible. The Tagus, Niger, and their prize the Ceres, sailed on to Rio Janeiro arriving there on the 2nd February. The Three Bees and the Catherine, both also armed, continued on their journey. They arrived at Rio Janeiro on 3rd February and while there entertained Portuguese Custom's Officers who had come on board to prevent smuggling. 
Rio de Janeiro
In the Harbour of Rio Janeiro, the convicts were all on the deck together every day. On which occasions the Mercury in the thermometer fell in the prison 6, 7 and 8 degrees. Here a case of fever appeared, and as it bore all the marks of common ship fever every precaution was used to prevent the contagion from spreading. The subject of the fever died. The Three Bees left Rio on the 17th February. 
During the voyage a gill of wine was issued every Sunday to each man, when at sea, till they drew nigh the end of the voyage, when it was served out twice a week. During the prevalence of cold, damp or rainy weather, fires were lighted in the prison. It was every morning cleaned and was fumigated with sulphuric acid and Nitre, as long as they lasted; when these failed camphor and vinegar were used. The convicts were formed into five divisions, each having a portion of the day on deck when the weather would admit. 
On the 27th February a strange sail appeared, and, as she bore down, had the appearance of an enemy. The prisoners' bedding was used on this occasion as a barricade and being kept on deck all night was quite drenched with rain. After several fruitless endeavours on as many days to dry the bedding, it was put into the prison; at the same time the prisoners were cautioned not to use it. This injunction was disregarded and scurvy, which had been long lurking among them, made its appearance. Seven men died of it ere they reached Port Jackson and fifty-five were sent to the hospital in a dreadful state. Nine (or ten) convicts died on the passage. 
The Three Bees arrived in Port Jackson on 6th May 1814 with 209 male prisoners.
Governor Macquarie wrote of the state of the Three Bees convicts in correspondence to Earl Bathurst dated 24 May 1814 - Out of those landed, it has been necessary to Send fifty-five to the Hospital many of them being much affected with Scurvy and others labouring under various complaints. On enquiring into the cause of this mortality and sickness, it appeared that many of them had been embarked in a bad state of health, and not a few infirm from lameness and old age.
The new hospital (the Rum hospital) was not finished until 1816 and the hospital the prisoners of the Three Bees were taken to would have been the old dilapidated hospital at Dawes Point where William Redfern was employed.
The Prisoners were landed on 11th May, and every man landed expressed gratitude for the indulgences during the voyage. On landing those who weren't taken to the hospital were sent to Windsor, Liverpool and Parramatta where they were to be assigned to settlers.
William Redfern's Recommendations
Having seen first-hand the result of the problems that had beset the voyages of the Three Bees, the Surry and the General Hewitt, William Redfern made several recommendations that had far-reaching effects on the well being of prisoners on convict ships including improved ventilation, diet and adequate clothing. On his recommendation all future convict ships would also employ a Surgeon Superintendent:
Captain Wallis and the Military Guard Enquiry
On arrival in the colony Captain Wallis preferred complaints against the Military Guard necessitating an official enquiry........
Captain Wallis' evidence commenced the proceedings.
Behaviour of the Officers before the Ships Log was commenced.... The Officers, having invited a party of their friends on board to dine, on my going ashore, I left orders that every civility and attention should be given by my ship's company to the Ladies and Gentlemen who might come on board in my absence which orders were complied with.
On my coming on board in the afternoon, the surgeon informed me that he was just sitting down to write a note to Mr. Miller of the impropriety of having a Fiddler on board on Sunday for the purpose of music or dancing. Astonished at this information, I sent for the Fiddler and ordered him to quit the ship immediately observing at the same time that I had no objections against music or any other amusements on other days and at proper hours, but that I would permit no such proceedings on Sunday and the more especially on board a convict ship where every officer should study the utmost regularity.
Sergeant Willington who by this time formed one of the party was employed during the evening in singing songs and repeating plays to a very late hour to the great annoyance and disturbance of the ship's Company on board. After the convicts came on board, the military officers, not giving that share of attention I judged necessary for the peace and security of the ship I deemed it necessary to make enquiry of the transport board what attention or duty they usually required from Military Officer commanding detachment on board convict ships -
To this application which I made on the 12the November I received an answer from the secretary of the Board dated 15th November stating that application had been made to His Royal Highness the Commander in Chief to cause immediate orders to be given to the Officers of the Guard over the convicts in the Three Bees for the proper security of ship and convicts. His Royal Highness in a few days after my receipt of the Secretary's letter advised the Governor of Pendennis Castle to reprimand the Military Officers on board for not having kept regular watch and to instruct them to do so in future.
Complaints entered in the Ships Log by the Chief Mate Benjamin Smith.....
1). 24 November on board laying in Falmouth Harbour. - Ensign Skelton who was intoxicated at the time, on being requested by the Captain to cease making unnecessary noise which was disturbing the ship's crew, told the Captain to go to Hell and be damned. (William Raynolds and Michael Buffery of the 46th regiment were on sentry duty on this evening.)
2). 16 January 1814 - at sea - the Boatswain Matthew Homan and several of the crew - William Gibson, John Josse, Stephen Pury, William Jones, John Thomas John Walters were found drunk having been given spirits by the Officers of the detachment unknown to the Captain or officers of the Ship.
3). At Rio de Janeiro - The Officers of the Guard, in a state of intoxication came on deck and Mr. Skelton and Mr. Wilson began to play the flute to the soldiers persuading Portuguese Officers of the Customs House to dance, giving them liquor and made them so drunk that some of them could not stand. The ships officers and crew were disturbed until midnight.
4). 10 March - at sea. At 8 pm, the ship silent, the Officers of the Guard, rather intoxicated came on deck, called for Dunscombe their servant, to bring Ensign Skelton his flute and he began to play. The Officers began dancing, making such a violent noise that the ship's company could not rest. Ensign Skelton stood with his back against Chief Mate Benjamin Smith's Cabin, who finding the noise so bad he was obliged to get his great coat and lay on top of the round house. When the Captain requested that the men 'leave off' making so much noise, Ensign Wilson began abusive language and threatened to horse whip the Captain.
5). April 8 - at sea. Sergeant Willington whose watch it was on deck was singing lewd songs and the Officers with him, making such a noise to the great annoyance of the sick in the half deck and to the part of the ship's Company whose watch it was. The ship's carpenter was at this time laying dangerously ill with dysentery and Mrs. Deverill was in child labour so that the surgeon was under the necessity of writing an official note. 
The enquiry mentioned above after hearing evidence from Captain Wallis, Chief Mate Benjamin Smith, Second mate Thomas Collins and Surgeon Thomas Andrews, then commenced with submissions from the military guard.......
Members of the Guard who gave evidence included William Raynolds and Michael Buffery who were on sentry duty on the evening of the 24th November; Private Barnard Brown; Private Patrick Coghlan and his wife Mary Coghlan; Sergeant Hugh Crocket; Sergeant John Deverell
Lieutenant Miller gave a lengthy written defence.......... Sergeant Willington was described by Lieutenant Miller - Sergeant Willington was known to most of the Officers for his theatrical talents and good voice, they were also aware that he has been brought into company before the Commander of the Forces in Jersey, Lieut General Dow, and contributed to his and his friends entertainment.
Lieutenant Miller also described the surgeon Thomas Andrews - This is a man who would pass for a religious character, he is the echo of his Master, was it his religion or Mr. Wallis's humanity that induced him to throw eight fellow creatures overboard without sending a single prayer over them for mercy and forgiveness of their sins. Was it religion Gentlemen prompted the sanctified sinner to take one of the women of my detachment into his hospital on pretence of curing her of some disease she had in consequence of a recent delivery - was it religion prompted him to attempt the virtue of this unfortunate woman enfeebled and worn down by sickness and sufferings - her screams fortunately brought her husband just in time to save her, he burst into the Hospital as this pious hypocrite was attempting his vile purpose and found him trembling with shame and confusion, this is a creature of the Master and a man who professes a large share of religion and humanity; these circumstances were reported to me and I have the man and wife ready to prove them.
Gentlemen, It will I have no doubt appeared to you that notwithstanding the humanity of the Master, he has all along been actuated by revenge and malignity towards me and my detachment. That he has made every effort in his power to make the situation while on board his ship wretched and that he has succeeded in drawing on us the censure of His Royal Highness, The Commander in Chief
The Court delivered its verdict on Monday 30th May 1814....... There is found to be no part of neglect of duty by Officers Thomas Miller, Hans Morrison and Ensign Hamilton. J. Wilson and John Skelton as Officers, but in such manner as excited by the presuming and unbecoming manner of Mr. Wallace (Wallis), the late Commander of the ship Three Bees to them. And that it appears the allegations preferred as not from any motive of benefiting the service, but from premeditated malignity from their earliest meeting. 
Notes and Links
1). George Plummer, carpenter, arrived free on the Three Bees (CSI)
2). The Three Bees was totally destroyed by fire on Friday 20 May 1814. Select here to read an article in the Sydney Gazette
3). Assistant Commissary-General John Palmer arrived as a passenger on the Three Bees....John Palmer first came free as Purser of the 'Sirius' on the First Fleet in 1788 and on 2 June 1791 was appointed Commissary; in September 1796 he left for England per 'Britannia', returning in November 1800 per 'Porpoise'; he went to England with Bligh as a witness in 1810, and was demoted to Assistant Commissary in 1811; in June 1813 he was re-employed in the Commissariat and returned to New South Wales (Colonial Secretary's Index)
4). George Marley was indicted for embezzling several sums of money, the property of Messrs. Fay, Grangler, and Hughes, of Navan, during the period he acted as their clerk in Drogheda by taking credit in his weekly accounts for money. The prisoner pleaded guilty and after received a lecture from the learned Judge, he was sentenced to seven years transportation. (Belfast Newsletter 5 March 1813)
5). Edward Dogherty was indicted for publishing as true, a forged note of the Belfast Northern Bank of one guinea and a half and also for forging the guinea and a half notes of Messrs. Ball and Co of Dublin and also for forging the Government stamp upon these notes. Evidence for the Defendant - Peggy Dougherty said she knows the prisoner by having seen him formerly at fairs, and recollects having met him in the beginning of October last, within three miles of Belfast, and when they walked on together she observed a lump of paper on the road which he picked up, and on opening it, found it contained Bank Notes. he would scarcely let her see it, but she claimed a part, which, however, he refused to give. Cross Examined - Q. Where do you live? A. Near Bunerana, and the prisoner lived some distance from that Q. Was you much acquainted with him? A. I have seen him at fairs, and I knew his father. Q. Is the prisoner your son? A. No. Sir, he is not a drops blood to me. Verdict - Guilty - Sentenced to transportation for seven years. (Belfast Newsletter 24 March 1812)
6). In the afternoon the Judge passed sentence on Dennis Hammill, convicted on Friday of highway robbery appointing him to be hanged on the 24th day of April. The prisoner fell down on his knees and entreated for mercy, saying that he would serve in the army or navy, but his Lordship tole him that he would not disgrace either of these by a man of so bad a character and exhorted him to prepare for death for that he need not look for mercy. (Belfast Newsletter 24 March 1812)
7). Mullingar Assizes - Administering of Oaths - Cornelius Maguire, a private in the North Cork Militia and Hugh Molloy, were tried on an indictment, charging that Hugh Molloy at Athlone, in the County of Westmeath, seditiously intending to disturb the public peace, did administer a certain Oath to James Connell, of said place; and that the said Corn. Maguire, with the like seditious intention, at Athlone, in the County of Westmeath aforesaid, was present, aiding and abetting; which said Oath was to the purport and effect following, that is to say; 'To be true to the Emperor of France, Napoleon; to assist the French forces in overturning the Government of Ireland; to plant the Tree of Liberty in Ireland till its branches reached the coast, and its leaves became united: against the Statute in such as made and provided, and against the Peace of our Sovereign Lord the King, his Crown and dignity. The Statute on which the indictment was founded by which the administering of unlawful Oaths for seditious purposes, or to disturb the public peace is punished by transportation for life; and the taking of such Oath is punished by transportation for seven years. The facts of the case were stated: James Connell, examined by Mr. Espinasse. Was then produced as a Witness, to support the Indictment, and he deposed to the following purport: That he and his family lived under Lord Castlemain near Athlone, hearing that there were seditious meetings in the neighbourhood of Athlone, he went to Lord Castlemain's house, and disclosed his suspicions to his Lordship, Lord Castlemain told him he was going to Dublin, for a short time, and advised him to make enquiry into the business, and to get himself sworn in to the association - that soon after he met with Hugh Molloy, and Cornelius Maguire, the soldier, and they went into a public house, kept by one Daly, in Athlone. After drinking some porter, Molloy entered into conversation about the times, took out a book, and administered an Oath to the witness - the soldier Maguire, he said, stood with his back to the door, and could hear and see everything that was going forward. - Molloy gave him a ticket and told him, by that he would be admitted into any Meeting of the Society. On Lord Castlemain's return to his seat, near Athlone, the witness said he waited on his Lordship and communicated the whole of what he had given in evidence......The Jury found both Prisoners guilty and they were sentenced to be transported for life. - Freeman's Journal 5 October 1813
Morgan Briant / Bryan
Henry Denny / Dinny
Patrick Hardiman / Hardigan
Patrick Murphy Newcastle
Michael Neal / O'Neil
 Colonial Secretary's Correspondence. State Records Authority of New South Wales, Kingswood. Main series of letters received, 1788-1825. Series 897, Reel 6044; 4/1730 pp.101-43