Bjeković spent seven seasons at Partizan, scoring 82 league goals in 198 appearances for the Black and Whites. He was the top scorer of the Yugoslav First League in the 1975–76 season with 24 goals, thus helping Partizan win their seventh national title, his first.
In the summer of 1976, Bjeković moved abroad for the first time in his career and signed with Nice. After playing five seasons in the French Division 1, he scored a total of 85 league goals in 143 appearances.
Bjeković started his coaching career in 1982 as an assistant coach to Miloš Milutinović at Partizan. After two years of gaining experience, he replaced Milutinović at the start of the 1984–85 season. As head coach of Partizan, Bjeković won two consecutive league titles in 1986 and 1987.
In 1987, Bjeković was appointed as head coach by his former club Nice, but was released after two years. In 1990, he again managed Partizan for two months.
After his coaching career, Bjeković served as a sporting director of Partizan for almost two decades from 1990 to 2007.