After spending his development years at local clubs Zemun and Teleoptik, Bogunović made his senior debuts with Srem Jakovo in the Serbian League Belgrade in 2003.
In the following season, Bogunović was the team's third-highest scorer with eight league goals, behind Filip Đorđević (16) and Brana Ilić (9), as Rad failed to earn promotion back after losing in the playoffs to BSK Borča.
With 13 league goals, Bogunović finished the season as the club's top scorer ahead of the likes of Brana Ilić (6) and Vladimir Jovančić (4).
[1] He made his competitive debut for the club in the first leg of the 2008–09 UEFA Champions League second qualifying round, on 29 July 2008, scoring the opener in a 1–1 draw away at Inter Baku.
After returning from loan, Bogunović helped Partizan qualify for the 2010–11 UEFA Champions League group stage, but failed to make his debut in the main competition.