Bradley served with the East Yorkshire Regiment and then the Machine Gun Corps during the First World War, transferring to the Royal Air Force in August 1918. He was appointed Officer Commanding Number. 14 Squadron in 1921 and Station Commander at Royal Air Force Northolt in 1930.
Promoted to group captain in July 1931, Bradley went on to be Senior Air Staff Officer at Headquarters Wessex Bombing Area in November 1931, Director of Equipment at the Air Ministry in 1935, Air Officer Commanding-in-Chief Royal Air Force Maintenance Command in 1938.
He continued in that role during the Second World War, though he moved on to be Deputy Air Member for Supply & Organisation in 1942 before retiring at the end of the war.