On March 19, 2012, the Oilers signed Bunz to a three-year entry-level contract.[2]
On March 22, 2014, Bunz was hit in the throat by a puck, leading to a life-threatening injury. He recovered from his injury without needing surgery and resumed his playing career.[3]
In the 2014–15 season, on April 2, 2015, Bunz made his NHL debut against the Los Angeles Kings. He substituted in for Ben Scrivens, who had given up 5 goals, to start the third period. Bunz surrendered 3 goals on 12 shots and the Kings routed the Oilers 8–2.[4]'