Bingham was a younger son of
Charles Bingham, 4th Earl of Lucan (1830–1914) by his wife Lady Cecilia Catherine Gordon-Lennox (1838–1919), daughter of the
5th Duke of Richmond. He was
commissioned into the
Royal Artillery as a
lieutenant on 28 July 1883, and was appointed
Aide-de-camp to the General Officer Commanding 3rd Infantry Brigade at
Aldershot in 1889. Promoted to
captain on 15 August 1892, he was attached to the Egyptian Army in 1893. He became Aide-de-camp to the Commander-in-Chief,
Madras later that year, and then Adjutant of the Prince of Wales Own Norfolk Artillery in 1899, with the rank of
major on 13 February 1900. In 1911 he became Chief Instructor at the
School of Gunnery. In retirement he became a
Justice of the Peace in
Buckinghamshire. ==Personal life==