Bedford was born on 24 December 1838,[2] and joined the Royal Navy in July 1852, at the age of 14. He saw early service in HMS Sampson and HMS Vulture, taking part in several of the operations during the Crimean War 1854–55. As a Commander he served in HMS Serapis when that ship took the Prince of Wales (later King Edward VII) on a tour of India in 1875. He was promoted to captain on 15 May 1876, and was flag captain in HMS Shah on the Pacific Station during action with a Peruvian ironclad in May 1877. From 1880 to 1883 he was engaged in administrative work as Captain of the Royal Naval College, Greenwich, but the following year he was back in command, this time as captain of the ironclad HMS Monarch. After a spell as captain of the cadet training ship HMS Britannia, he joined the Board of Admiralty as Junior Naval Lord in December 1889, serving until August 1892.[3]
Bedford was back at the Admiralty as he was appointed Second Naval Lord in May 1895, serving as such until May 1899. He was promoted to vice-admiral on 10 May 1897.[5]
Bedford was announced as Governor of Western Australia in early January 1903,[3] appointed later the same month,[16] and formally took up the post on arriving there on 24 March 1903.
On 4 June 1907 he officiated at the opening of the Royal Fremantle Golf Club in Western Australia, but it was not until March 1909 that the complete 18 hole course was available.
Bedford married Ethel Turner, daughter of E. R. Turner, of Ipswich, in 1880. Lady Bedford accompanied her husband and was mistress of Admiralty House in Halifax, Nova Scotia, until 1902. She took an interest in benevolent work, and frequently performed as a singer at concerts, for charitable purposes.[18]
The couple's son was Vice Admiral Sir Arthur Edward Frederick Bedford, who married Miss Gladys Mort of Sydney, Australia. While residing at Easthampnett, their son Frederick, named after his grandfather, who had become a lieutenant in the Fleet Air Arm, was killed in action over St Pauls Bay, Malta on 21 February 1942, aged 22 years, and was buried in Capuccini Naval Cemetery in Kalkara, Malta.
Bedford authored a publication entitled The Sailor's Pocket Book: a Collection of Practical Rules, Notes, and Tables. For the Use of the Royal Navy, the Mercantile Marine, and Yacht Squadrons. The book was first published in 1875.[20] A 4th edition was published in 1885.[21]