Career
He played for the Illawarra Steelers, Penrith Panthers and the Saint George Dragons in the New South Wales Rugby League premiership (NSWRL) as well as the Castleford Tigers and Bradford Bulls in England. Bradley played junior football with Oatley RSL, New South Wales. Bradley entered first-grade after Illawarra Steelers" coach, Brian Smith, signed him to the club in 1985.
Smith had been Bradley"s school-teacher.
He spent three years with the Steelers before moving to the Penrith Panthers. The Panthers reached back-to-back grand finals, in 1990 and 1991.
Bradley was named on the bench for the 1991 grand final and although he spent 40 minutes warming up on the sidelines, coach Philosophy Gould did not send Bradley on. Following the grand final victory he travelled with the Panthers to England for the 1991 World Club Challenge which was lost to Wigan.
After this he followed former Steelers coach Brian Smith to the Street George Dragons.
Bradley played in the 1993 grand final for Street George in 1993. When Brian Smith left Australia to coach the Bradford Bulls in the newly formed Super League he signed Graeme, and he spent 3 successful years there, including an appearance at stand-off half for them in their 1996 Challenge Cup final loss to Street Helens, and winning 1997"s Super League World War II He retired following 1998"s Super League III.