[4] Bunting made the jump to the Coyotes' professional ranks in the 2015–16 season with the Springfield Falcons of the American Hockey League (AHL).

The Coyotes briefly assigned him to the ECHL's Rapid City Rush early in the season where he scored his first professional goal, before returning him to Springfield.

[10] Bunting scored his first NHL goal in his debut, beating Boston Bruins goaltender Tuukka Rask in the second period of a 4–3 Coyotes loss on December 11, 2018.

He registered a goal and an assist in his season debut, a 9–3 Coyotes loss to the Colorado Avalanche,[17] before scoring his first NHL hat-trick against the Los Angeles Kings on April 5, 2021.

[17] As a group 6 free agent after breaking out with the Coyotes, Bunting was signed to a two-year, $1.9 million contract with the Toronto Maple Leafs on July 28, 2021.

[19] He left the Coyotes franchise being the Roadrunners' all-time leader in games played, goals, assists, points, and penalty minutes.

In late December, Bunting was aggressively shoved off the ice by an official while being assessed a minor penalty, stirring a small controversy.

[26] After a build up of what some commentators had perceived to have been light calls against over the next several months,[27] Bunting's relationship with the referees came to heightened media attention after he was assessed a 10 minute major penalty and a game misconduct for skating into an opposing players' dropped stick during a match on April 2, 2023.

[31] He made his debut with Carolina on October 13, 2023, scoring the Hurricanes' first goal of the game against Joonas Korpisalo in a 5–3 win over the Ottawa Senators.

[35] On March 7, 2024, Bunting was traded to the Pittsburgh Penguins, along with Ville Koivunen, prospect Cruz Lucius, Vasili Ponomaryov and two conditional 2024 draft picks, in exchange for Jake Guentzel and Ty Smith.

[39] Team Canada general manager, Roberto Luongo, invited Bunting to participate at the 2021 IIHF World Championship following the 2020–21 season, giving him his first opportunity to represent his home country on an international stage.

[42] Following the end of the 2023–24 NHL season, with the Penguins not qualifying for the 2024 Stanley Cup playoffs, Bunting rejoined the senior national team for the 2024 IIHF World Championship.