Robert Arthur Buddicom was born in Shropshire, England, on 7 November 1874. He was educated at the University of Oxford where he studied biology and physiology and acquired an Honours degree. He was the curator of the Plymouth Museum and Art Gallery from 1900-1901 and later worked as a demonstrator and lecturer at the London Hospital Medical College (1906-1914). After court action in England over a failed business venture, he migrated to Australia with his wife and children in 1915 and changed his surname to Bedford. He settled in Kyancutta on Eyre Peninsula in South Australia.

In Kyancutta Robert Bedford worked as a physician and veterinary surgeon, and also operated the local weather station. He was interested in palaeontology and meteorites and travelled widely in South and Central Australia, collecting fossils, meteorites and other natural history specimens. In 1929 he opened the Kyancutta Museum and Library to house his large collection of ethnological, faunal and geological specimens. He was an outspoken advocate of what he called 'country museums' and this led him to some conflict with other Museum authorities.

During the 1930s Bedford published a journal The Memoirs of the Kyancutta Museum which included his own papers on palaeontology, philosophy and other scientific topics. He also published pamphlets on morse code, freedom of religion and other matters.

Bedford died on 14 February 1951. Some of the specimens from his museum were acquired at auction in Sydney in 1972 by the South Australian Museum.

The Barr-Smith Library at the University of Adelaide has a large collection of Bedford's manuscripts, notes and other records relating to his interests in natural history, meteorites, palaeontology and Egyptian antiquities.