Bradley played junior hockey in the Thunder Bay Junior Hockey League for the Port Arthur West End Bruins from 1946 to 1949, winning the playoff championship in 1948 and 1949 as well as the 1948 Memorial Cup. He turned pro in 1949 and signed with the American Hockey League's Hershey Bears, but was called up to play one game for the Boston Bruins, which turned out to be his only game in the National Hockey League. He spent time in the United States Hockey League for the Tulsa Oilers and the Pacific Coast Hockey League with the Tacoma Rockets followed by a seven-year tenure in the Western Hockey League, beginning with the Rockets who only lasted one season. He then spent time with the Seattle Bombers, New Westminster Royals, Victoria Cougars and the Seattle Americans.