Bougoure was a still a boy when he left his home in Dalby, Queensland, to pursue a career as a jockey at racetracks in the Brisbane area.
In 1945 he won his first major race and went on to win a number of premier events including two editions of the Australian Cup.
In the late 1950s Bougoure returned to race in Europe where his association with trainer Vincent O'Brien and Paddy Prendergast helped make him one of the top jockeys in Ireland and England during the first half of the 1960s.
Bougoure's numerous wins in Ireland include the 1960 and 1963 runnings of the Irish Derby and in England he won three of the Classics, taking the 1963 Epsom Oaks with the filly Noblesse, the 1963 St. Leger Stakes with Ragusa and in 1964 the 1,000 Guineas Stakes aboard Pourparler.
He then embarked on a career in training that would last several decades until leaving the sport completely in 1995 at age seventy-three.