Bowrey was the last amateur to win the Australian Championships in 1968 before the tournament opened itself up for professional tennis players in 1969.

He was a quarterfinalist on three occasions (1966, 1967 and 1969) and doubles runner-up (with fellow Australian Owen Davidson) in 1967.

Also with Davidson, he reached the US finals in 1967 and Wimbledon in 1966.

Bowrey won the Italian mixed doubles title with his future wife, Lesley Turner, and played Davis Cup for Australia in 1968 and 1969, winning two singles and losing two against the USA and Mexico respectively.

Bowrey later worked as a Tennis Australia Talent Development coach mentor.