Bowrey was born in Sydney, Australia and is best remembered as the last amateur to win the Australian Championships in 1968[2] before the tournament opened itself to professional tennis players in 1969.

In 1966 he won the Sydney Metropolitan Grass Court Championships defeating Phil Dent, Dick Crealy, and Tony Roche in the final.

This reduced the quality of the field lined up for the 1968 Australian championships, which were held at Melbourne's historic Kooyong Lawn Tennis Club.

Defending his Australian title the following year Bowrey defeated Pancho Gonzales in the third round to reach the quarterfinals where he lost a two sets to love lead against Ray Ruffels.

[8] Later that year Bowrey with partner Marty Riessen won the Rogers Cup (formerly Canadian Open)[9] in two sets against Fred Stolle and Cliff Drysdale.

In February 1974, Bowrey won the New South Wales Hardcourt Championships, defeating Mark Edmondson in the semi-final and Stolle in the final in a close match.