Born in Banja Luka, but spent his childhood in Kraljevo, he started out at local club Čibukovac.
He also spent some time at OFK Beograd, before joining the youth system of Partizan.
In the summer of 2015, Bošnjak was promoted to the first-team squad in preparations for the 2015–16 season.
In July 2018, Bošnjak was loaned to Serbian SuperLiga club Zemun.
In the meantime, he played one season each in Voždovac and Kolubara before he returned to his hometown and signed for Borac Banja Luka in September 2021.