Bryne was commissioned lieutenant on 14 September 1762 and promoted commander of the Pomona 18 on 21 January 1771, serving out of Lough Swilly and in home waters. During April 1773 he went out to the Mediterranean and after sending in reports relating to the French fleet at Toulon and Spanish fleet at Cartagena he returned home to have his ship paid off in August.
He was posted captain of the Hind 28 on 20 November 1775, commanding her on the Leeward Islands station and being a virtual prisoner aboard his vessel at Antigua to avoid writs arising from the impressment of local men serving in unauthorised privateers. In June 1777 he was ordered home with a convoy, and he arrived at the end of August.
In September 1777 Bryne commissioned the new Andromeda 28 in which he returned to North America prior to giving passage home to General Sir William Howe in May 1778, in the course of which voyage he captured and set afire the rebel privateer Angelica. He fought at the Battle of Ushant on 27 July 1778 and saw service in the Channel fleet during the summer of 1779, and after further employment in the North Sea during the autumn he went out to the Leeward Islands with a convoy on Christmas Day. . The Andromeda was present at the Battle of Martinique on 17 April 1780, and in the Leeward Islands campaign of May-July.
Captain Bryne and most of his crew died in the great hurricane of October 1780, with the Andromeda being wrecked on Martinique on the 11th.
His widow, Maria, had issue a son, Thomas Henry Mackenzie, with the Scottish-Russian Admiral Thomas MacKenzie, the child being born on 1 November 1782 and rising to the rank of commander in the British Navy.