Bajramović spent the early part of his career in his native Bosnia and Herzegovina between his original club, Čelik Zenica and Bosna Sarajevo, with whom he won the national title and cup in 2005.

In June 2008, he signed a two-year deal with the Ukrainian team BC Kyiv.

[13] However he played only one game with Spars, and on February 1, 2014, he signed with Beşiktaş İntegral Forex of Turkey for the rest of the season.

[16] On February 19, 2016, he left Spars and signed for the rest of the season with Socar Petkim of the Turkish Basketball First League.

[17] On August 12, 2016, Bajramović signed with French club Cholet Basket for the 2016–17 season.

[21] Bajramović is a long time member of the Bosnia and Herzegovina national basketball team.