Bristol, named after the eponymous port, was ordered on 12 October 1768 to a design by John Williams. The ship, however, was not laid down until May 1771 at Sheerness Dockyard and was launched on 25 October 1775. Commissioned that same month, she cost £23,440 to built and a further £3,574 to outfit.
During the American War of Independence, she was Commodore Sir Peter Parker's flagship during the attack on Sullivan's Island on 28 June 1776 and was heavily damaged during the battle. Later in the war, she was stationed off Jamaica, and fought at the Battle of Cuddalore. After 1794 she was used as a prison ship (lying in Gillingham Reach, in the County of Kent), and was broken up in June 1810 at Sheerness.