The Hancock family established a homestead and farm at the foot of the Adelaide Hills in the mid 19th century. A family name from an earlier generation lent its name to the property of Bedford which was later changed to Bedford Park. In 1917, 400 acres (1.6 km2) of the property was purchased by the South Australian Government and a tuberculosissanatorium was built. Initially housing World War Isoldiers the sanatorium was expanded until, by 1924, it had 74 beds and was a self-supporting farm with pigs, chickens, orchards and grain production. The sanatorium was demolished and Flinders University built in its place in the 1960s.
Burbank Post Office opened on 26 September 1961 and was renamed Bedford Park in 1966, before closing in 1980.