He previously played college ice hockey for Western Michigan University in the National Collegiate Athletic Association (NCAA).

Bussi committed to playing college ice hockey for the Western Michigan University during the 2019–20 season.

On March 30, 2022, the Boston Bruins announced that Bussi would forgo his senior year to sign a one-year, entry-level contract with the team.

Throughout the season, Bussi was occasionally called up to the NHL team on an emergency basis, due to injuries to Boston goaltenders Jeremy Swayman and Linus Ullmark.

At seasons end, for the second consecutive year, the Providence Bruins were set to face the Hartford Wolf Pack in the first round of the Calder Cup playoffs.