Career
Bubnjić started his career playing at youth level for Daruvar, before moving to the Slaven Belupo youth team in 2007. In the first part of the 2011-2012 season, he was loaned to Treća HNL side Koprivnica where he was featured in 13 games scoring two times. He scored his first goal in Prva HNL in a 1–1 draw with Rijeka on 6 May 2012.
In September 2012, it was announced that Bubnjić signed a five-year contract with Udinese, but will remain at Slaven until the end of the season.