He was born on 12 October 1816 in Edinburgh, the son of Janet Gillespie (1788-1858) and Robert BrysonFRSE (1778-1852), a watchmaker.
He attended the High School in Edinburgh then trained as a watchmaker and entered the family business, then renamed Robert Bryson & Son.[3]
With his first wife, Elizabeth Waterstone Gillespie (possibly a cousin) he had two children who died in infancy, and a daughter and son (William Alexander Bryson) and died 10 April 1855 aged 44.
His second wife, Catherine McDonald Cuthbertson, also died young in September 1859, aged 32. Together they had a son. With his third wife, Jane Thomson, he had another son, Leonard Horner Bryson, who survived him and remarried.
He was President of the Society of Antiquaries of Scotland 1860–1861. He was President of the Royal Physical Society of Edinburgh in 1863. He was also a member of the Botanical Society of Edinburgh and the Edinburgh Geological Society.