Bunnaman was drafted in the fourth round, 109th overall, by the Philadelphia Flyers in the 2016 NHL Entry Draft. Upon being drafted, Bunnaman stated that he felt he would fit in well with the team because he considered himself "a two-way, power forward. I create space well for others so I think I fit into their system well." Prior to the 2017–18 season, Bunnaman signed an entry-level contract with the team and was invited to participate in the Flyers' training camp. Upon returning, Bunnaman was named captain of the Kitchener Rangers alongside alternate captains Adam Mascherin, Connor Hall and Jake Henderson. At the night of the announcement, Bunnaman also played in his 200th career OHL, tying Barry Duench for 41st place in franchise history for regular-season games played.