Bingham joined the Royal Navy in 1781 as a midshipman on HMS "Dublin" and took part in the relief of Gibraltar. In January 1793 while serving as third lieutenant on HMS "Ganges" he assisted in the capture of Le Général Dumourier and other ships, and received his portion of a large amount of prize money. In May 1794 while serving as first lieutenant on HMS "Audacious" he was involved in engaging with La Révolutionaire and his good conduct was reported to the Admiralty.