His son Richard Hussey Bickerton, who likewise rose to flag rank in the Royal Navy, succeeded to the baronetcy following his death.

[1] Educated at Westminster School,[1] he joined the navy in 1739 and served aboard Suffolk, Stirling Castle, St George, Duke, Victory and Cornwall,[2] before being commissioned as a lieutenant on 8 February 1746 at the age of 18.

He subsequently commanded the Royal yacht Princess Augusta, and from October 1776 the 74-gun third rate Terrible; while aboard the latter he captured the American privateer Rising States on 15 April 1777 while cruising off Ushant.

In early 1780 Bickerton took command of the new 74-gun Fortitude,[1] and later was re-appointed to the Royal yacht Princess Augusta, before hoisting his broad pendant — as a commodore — aboard the 80-gun Gibraltar in January 1782.

[1] Returning to England upon the conclusion of hostilities, he hoisted his broad pendant aboard the 50-gun fourth rate Jupiter for a brief period as Commander-in-Chief on the Leeward Islands Station in 1786.