Bujak started his career in the youth squads of NK Čelik Zenica eventually breaking into the first team.
However, faced with little playing chances, he moved to FK Leotar Trebinje where he became a prolific goalscorer in the Yugoslav Second League.
He eventually found his way back to NK Čelik Zenica and was an integral part of their successes in the first few seasons of the independent Bosnia & Herzegovina.
During the 1994 season and the final tournament held in Zenica, he was the joint top goalscorer together with Dželaludin Muharemović with 3 goals.
Bujak has been a loyal servant to NK Čelik Zenica coaching the senior and youth teams at the club since the second part of the 1997/98 season.