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Stafford was born to parents Alfred Percival Bullen and Lilian Bullen, who in 1920 founded Bullen's Circus. Stafford's circus career began at four. Stafford travelled the country as a child with the circus. He had a tutor and was an above average student, yet his formal education ceased at age fourteen.
Stafford, along with his brother Ken Bullen, ran the family business after their mother died in 1965. In 1968 they opened the African Lion Safari. It attracted over two hundred thousand visitors annually. In 1969 Bullen's Animal World opened at Wallacia, New South Wales.
Stafford married Cleo; they had four children: Mark, Brenton, Sonya and Craig.
Currently Brenton runs the business of training animals such as lions, tigers and monkeys for media performance. Brenton lives at Australia Zoo with three of the elephants that he grew up with: Siam, Sabu and Bimbo.
- Tabakoff, Jenny (2001-01-12). "The Big Top was home and he had no wish to leave". Sydney Morning Herald. Archived from the original (obituary) on unknown date. Retrieved 2007-12-06. Check date values in: