After completing his formation at Rad, Bulatović made his senior debut with Dorćol in the 2009–10 Serbian League Belgrade.
He later spent two seasons with Serbian SuperLiga club BSK Borča from 2011 to 2013, making 21 appearances and scoring twice.
In the summer of 2014, Bulatović moved to Montenegro and signed with Budućnost Podgorica.
In the summer of 2023, Bulatović took over as manager of Serbian First League club Sloboda Užice.
[1] His father, Branko Bulatović, was general secretary of the Football Association of Serbia and Montenegro at the time of his assassination in 2004.