Bajević was the total player. He played almost 400 games for local club Velež Mostar where he scored 170 goals. His coach was Sulejman Rebac. Bajević is also remembered for being the part of the Velež three known as the "Mostar BMV" (Bajević, Marić and Vladić) during the 1960s, 70s and 80s. He stayed in Velež from 1966 to 1977 before going to AEK Athens, where he won the Greek championship twice. He is one of the most controversial figures in the history of the club. Bajević was a successful player, loved by AEK's fans who gave him the nickname "Prince" ("Πρίγκηπας").