When Britain entered the French Revolutionary War in 1793, Bickerton joined the Channel Fleet before, in October 1794, being ordered to transport General Sir John Vaughan to the West Indies, to take command of British land forces there.

After another spell in home waters, Bickerton was sent to the Mediterranean where he spent much of the war on blockade duty and, after their surrender, oversaw the evacuation of French forces from Alexandria.

[3] On 2 January 1815, Bickerton was made a Knight Commander of the Order of the Bath then later, in May 1823, he inherited the estate of Wood Walton and on doing so began using his mother's maiden name before his own surname.

[1][5] Subsequently, promoted to midshipman, he served under Captain William Affleck in the Mediterranean, returning home in 1777 on board Invincible, commanded by Hyde Parker.

[1] Bickerton was promoted to lieutenant on 16 December 1777 and served under Charles Middleton first on board the 90-gun HMS Prince George, then the seventy-four, Royal Oak in March 1778.

[5] On 20 October Jupiter attacked the much larger French ship-of-the-line Triton, forcing her to retire; as a reward for his conduct, Bickerton, on Middleton's recommendation, was in March 1779, promoted master and given command of the sloop, HMS Swallow.

[7] While on convoy duty during the Summer of 1779, Bickerton gave the order to disperse, having heard of the arrival of the combined Franco-Spanish fleet in The Channel.

[5][7][Note 1] After service in the Leeward Islands and North American waters, Bickerton returned to England in Amazon, arriving in Portsmouth in February 1782.

[5] Bickerton returned home in November 1795 where he joined Admiral Adam Duncan's fleet on blockade duty in the North Sea.

[3][5][Note 2] Bickerton hoisted his flag in Seahorse on 13 May 1800 and was ordered to transport generals Abercromby, Moore and Hutchinson to the Mediterranean; after which he spent the rest of the war under Lord Keith, on blockade duty.

[14] On 31 July 1810 Bickerton attained the rank of full admiral[15] and in March 1812 he left the Admiralty Board[13] and, one month later, was appointed Commander-in-Chief, Portsmouth[16] with Puissant as his flagship.

[21][22][23] Bickerton Island off the east coast of Australia's Northern Territory was named for him by the British navigator and cartographer, Matthew Flinders, who was the first to circumnavigate the continent.