[1] Born in Zenica, SR Bosnia and Herzegovina, SFR Yugoslavia, Bolić started playing with local NK Čelik, being one of the players in the club that would later represent the independent Bosnian national team, including Senad Brkić, Mirsad Hibić and Nermin Šabić.

In December 1991, Bolić was acquired by Yugoslav powerhouse Red Star Belgrade – defending champions of the European Cup – after impressing managers Vladimir Cvetković and Dragan Džajić.

[4] While at the Yugoslav national side's training camp in France, in June of the following year, 21-year-old Bolić received bad news from his family about the deteriorating situation in Bosnia and the start of the military conflict.

He informed the club's directors that he would not be coming back to Belgrade, and he left to Turkey to meet with his agent; Red Star respected his wish, and he subsequently signed with Galatasaray SK.

On 30 October 1996, Bolić broke Manchester United's 40-year unbeaten home record playing for Fenerbahçe in Europe when he scored the game's only goal at Old Trafford in the season's UEFA Champions League group stage,[6] where he also netted against SK Rapid Wien (1–1 away draw).