Alexander Bryson was born in Renfrewshire, Scotland in 1802 . He began his professional studies at Edinburgh and continued at Glasgow where he took his doctor's degree and was admitted a member of the Faculty of Physicians and Surgeons. He also became a fellow of the Royal College of Physicians, London. He entered the navy as assistant surgeon in 1827.
He was appointed Assistant Surgeon to the Castor in 1832 and the Griffon in October 1832 and spent almost a decade serving off the coast of Africa.....In 1836 the crew of the Griffon, on the paying off of the vessel, testified their gratitude to Alexander Bryson for his attention to them when in a state of sickness in the river Gambia, by presenting him with a full dress coat, epaulette, and strap, cocked hat, and sword; the latter with an appropriate inscription. .
Promoted to Surgeon
Alexander Bryson was promoted to the position of Surgeon in 1836 and was on the List of Surgeons of the Royal Navy who were fit for service in 1841.
He was appointed to H.M.S. Salamander at Woolwich on 21 September 1837. H.M.S. Salamander was a steam vessel, 220 horse power, built at Sheerness in 1832. 816 tons. Commander Hastings R. Henry. Assistant Surgeon John H. Patterson. 
He was appointed to H.M.S. Madagascar in 1841
He was employed as Surgeon Superintendent on the convict ship Marquis of Hastings to Van Diemen's Land in 1842. He kept a medical journal from 17 June to 30 November 1842. He recorded that the convicts were received at Portsmouth from the Hulks York and Leviathan - 120 from each, all apparently in good health. Those from the York were the first to show scorbutic symptoms - probably her position off Haslar Creek may have had some influence in this. Two prisoners died on the passage and all the others were landed although not quite free from Scorbutus, in good health and able to proceed on the instant to the out stations.
He was appointed Surgeon to the William and Mary in 1845 
In 1850 he published On the Respective Value of Lime Juice, Citric Acid and Nitrate of Potash in the treatment of scurvy - (Instructions were given several years ago to the surgeons of convict ships, that if scurvy broke out during the voyage, they were to try the relative effects of lime-juice, nitrate of potash, and citric acid; choosing similar cases for experiment, and placing the patients under like circumstances of diet and exercise. Dr. Bryson details some results which have been thus obtained.) ...........(continued)
He was head of the department of naval medical statistics and compiled the Statistical reports on the Health of the Navy and an article 'On medicine and Medical Statistics'
Deputy Inspector of Hospitals
In 1854 the Morning Post announced that Alexander Bryson, serving as surgeon of the Fisgard, flag ship at Woolwich was appointed Deputy Inspector of Hospitals. It was expected that he was to be ready for service in a hospital ship about to be commissioned for the purpose of accompanying the fleet under the command of Vice Admiral Sir Charles Napier K.C.B. 
Honorary Surgeon to Her Majesty
He was appointed Honorary Surgeon to Her Majesty in November 1859 (Caledonia Mercury)
In the 1861 Census he was recorded as residing at Hermitage, Barnes, Surrey. He was unmarried and age 58. His niece Mary Bryson was a visitor at his residence and he employed a cook and a housemaid.
Director-General of the Medical Dept. of the Navy
He was appointed director-general of the medical department of the navy on the retirement of Sir John Liddell in January 1864  and made a companion of the Order of Bath.
His death was announced in the Glasgow Herald in December 1869 - At the Hermitage Barnes, London on 12th instant, Alexander Bryson, M.D., C.B., F.R.S., Honorary Physician to the Queen, late Director General of the Medical Department of the Navy, aged 67.
His obituary was published in the Lancet -
Dr. Bryson, though a valuable public servant in his own peculiar line, was neither an efficient nor a popular Director-General. An officer, however zealous, who has never done duty as a deputy-inspector or inspector of hospitals ought to be, and for the future we are happy to know ill be, held unfitted for promotion to higher rank; and it is no disparagement to Dr. Bryson's memory to say that he was by education totally unfitted to cope with the many difficulties of a Director-General's position. Statistical details of the Department had always the greatest interest for Dr. Bryson; but a question affecting the position of a medical officer, in some dispute with a commanding officer, received from him no sympathy or attention; and the member of the naval medical profession felt that they had no real chief to represent their interests at head quarters, and to defend them against the encroachments of the executive.
Dr. Bryson was, however, as we have said, a valuable public servant, if placed in a false position; and he certainly deserved better treatment than he received at the hands of the present Admiralty. Sudden notice to vacate office was accompanied by an order to continue to do the duty of the department until, at the convenience of the authorities, a successor was appointed, and was followed, without the slightest reference to or consultation with the Director-General, by the appointment of a commission of civilians to inquire into and overhaul the great naval medical establishments of the country. Then came the question of pension, and the public will hardly believe that this question was still being fought with Admiralty when death stepped in and cut the matter short.
That the slights to which he was subjected, including the refusal of the knighthood ordinarily given to a Director-General, had an effect upon Dr. Bryson's health is unquestioned. During the past summer he consulted Dr. Russell Reynolds on account of noises in the ears, deafness, pain in the back of the head, and confusion of ideas, which, at times, troubled him much, but from which he recovered by rest and other measure. On Thursday the 9th instant, Dr. Bryson seemed remarkably well, and in the afternoon was walking in his garden in good spirits and apparent health. But, on coming into the house he felt suddenly ill, became strange in manner and then became unconscious.......his right side was found to be completely paralysed and he remained in a coma until death on the Sunday morning
 The Morning Post 15 August 1836
 Hampshire Advertiser 18 January 1845
 The Morning Post 2 March 1854
 Dictionary of National Biography Volumes 1 - 20
 Ancestry. 1861 England Census [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2004
 Haultain, C. (compiled), The New Navy List, 1840, p. 220