Rudolph was the second son of Walter Theodore Edward Bentinck, 13th Baron Bentinck (1840–1901), of a distinguished Dutch family, by his wife Henrietta Jane Christina (d. 1924), daughter of William Hinton, of The Til, Madeira, Portugal.
[2] Bentinck served in the First World War, taking part in the Battle of Jutland in 1916, as Chief of Staff to Admiral Sir David Beatty,[4] and being mentioned in despatches.
[2] He was appointed second-in-command of the 1st Battle Squadron in the Atlantic Fleet in 1921 and went on to be Commander-in-Chief of the Africa Station in 1922.
[2] In that capacity he was briefly acting Governor-General of South Africa from December 1923 to January 1924.
[5] Bentinck became Admiral Commanding the Reserve Fleet in March 1926 and then Commander-in-Chief, Plymouth later that year: he retired in 1929.