He was one of the surgeons who examined the body of the journalist William Jackson after he died from poisoning in a Dublin court in 1795 while awaiting sentencing for high treason.

His father was Robert, and his grandfather was Thomas Hume, of Humewood, County Wicklow, who was an ancestor of the Irish Conservative politician William Wentworth Fitzwilliam Hume-Dick.

He liked to prescribe oatmeal porridge and as a result received the nickname "Stirabout Gusty" which was referred to in William Norcott's The Metropolis as follows:[2] Hume was one of 49 physicians and chirurgeons who declared their public support for the construction of a Publick Bath in Dublin in May 1771 and named Achmet Borumborad as a well qualified individual for carrying such a scheme into existence.

[2] Hume was president of the RCSI only from January to 4 May 1795, resigning on that date for reasons that are unknown but which Cameron writes probably related to the case of the former member of the society, Frederick Drury, who was expelled for giving false testimony in court.

[9] He built a mansion in Merrion Square to a design by Samuel Sproule, which was later divided into two large houses, in one of which Sir John Banks, physician to Queen Victoria, lived.