Despotovski was born in Perth, Western Australia, to a Macedonian father, Cvetko, and mother, Valentina (Saharov).

Despotovski was with the Western Australian team Perth Glory for 10 years, and holds their all-time goal scoring record.

Despotovski finished the season as joint top goal scorer of the league and winner of the Johnny Warren Medal.

[10] Season 2006/2007 started without Bobby because of his re-occurring back injury but he returned to partner Stuart Young up front.

Despotovski played 4 games for Australia, three of them at the 2002 OFC Nations Cup where he blasted four goals past the New Caledonia goalkeeper.