1732-82. He was the second of three sons of Professor Alexander Bayne, an Edinburgh lawyer who moved to London before returning to Scotland, and of his wife, Mary Carstairs. His elder sister married the painter Allan Ramsay, who after her death in 1743 notoriously eloped with the sister of the future Admiral Sir Charles Lindsay.
On 5 April 1749 Bayne was promoted lieutenant, and in 1755 served in North America with Vice-Admiral Hon. Edward Boscawen?s squadron aboard the flagship Torbay 74, Captain Charles Colby. He was promoted to command the sloop Spy 10 on 10 November 1756, taking despatches to New York in the following spring and then cruising the year after. During 1759 he served in Commodore John Moore?s attack on Martinique, which was aborted, and Guadeloupe, which was successful.
On 1 July 1760 he was posted captain of the Woolwich 44 after commanding her for some time since the death of Captain Daniel Deering, being employed on a cruise before going out to Africa and the Leeward Islands. Here he served at the reduction of Martinique in early 1762 and took the privateer Dame Auguste on 7 February. Thereafter he had the frigate Stag 32, serving under Rear-Admiral George Rodney?s orders in the Leeward Islands and at Jamaica in 1763 before being paid off in May 1764.
For the next fourteen years Bayne remained unemployed until in the autumn of 1778 he commissioned the brand new Alfred 74 at Chatham. In April of the following year he sat on the court martial of Vice-Admiral Sir Hugh Palliser in the wake of the Battle of Ushant on 27 July 1778. He was present in the Channel during Admiral Sir Charles Hardy?s strategic retreat of August 1779 and fought at the Battle of St. Vincent on 16 January 1780. Then having participated in the latter stages of the Channel Fleet?s campaign between July and December he sailed with a squadron under the command of Rear-Admiral Sir Samuel Hood for the Leeward Islands in January of the following year, and was present at the capture of St. Eustatius on 3 February. .
He subsequently led the line at the indecisive Battle of Fort Royal on 29 April 1781 and at the Battle of Chesapeake Bay on 5 September where, due to the rigid interpretation of the standing fighting instructions, his ship was unable to take an effective part. The Alfred returned to the Leeward Islands with Hood in the autumn, but in January 1781 she was involved in a collision with the frigate Nymphe 36, Captain John Ford, off St. Kitts. Nobody was held accountable for the incident and indeed Bayne earned great praise for quickly restoring the Alfred to order and joining Hood?s repulse of the French at that island on 25/26 January 1782.
Whilst leading the British line in the skirmish with the French fleet on 9 April, prior to the Battle of the Saintes on 12 April, Bayne?s leg was carried off at mid-thigh by a chain shot and he died before a tourniquet could be applied.
A monument in Westminster Abbey commemorated Bayne and Captains William Blair and Lord Robert Manners who also lost their lives through wounds incurred at the Battle of the Saintes. He had never married.