Bussi's journey from an undrafted goalie from Sound Beach, New York, to the NHL hit another high note when he signed a three-year, $5.7 million contract (average annual value of $1.9 million) with the Carolina Hurricanes on Feb. 16, 2026. To celebrate the deal, the Carolina Hurricanes Foundation made a $10,000 donation to the Autism Society of North Carolina. Bussi's younger brother, Dylan, has autism, and Brandon's goalie mask is a tribute to Dylan meant to raise awareness.

At age 27, Bussi was 23-3-1 with a 2.11 goals-against average, .920 save percentage and two shutouts when he signed the contract. He earned his 21st NHL win with 11 saves to defeat the Los Angeles Kings 3-2 in Raleigh, North Carolina, on Feb. 1, surpassing Andrew Hammond (20-1-2) and Bill Durnan (20-2-3) for the most by a goalie through his first 25 NHL games. He was claimed by the Hurricanes off waivers from the Florida Panthers on Oct. 5, 2025, as insurance for Frederik Andersen and Pyotr Kochetkov, and made his NHL debut Oct. 14 with Kochetkov missing the start of the season because of lower-body injury. Bussi made 16 saves in a 5-1 victory against the San Jose Sharks.

Bussi made 22 saves in Game 6 of the 2026 Stanley Cup Final to win the Stanley Cup when the Hurricanes defeated the Vegas Golden Knights 3-0, the shutout the ninth in a Cup-clinching game in the past 50 years and first since Andrei Vasilevskiy for the Tampa Bay Lightning in 2021. He stopped 81 of 87 shots after taking over for Anderson in Game 3 and went 3-1 with a 1.60 GAA and .931 save percentage. That made him the first goalie since 1975 (when the Preliminary Round was introduced) with a title-clinching win after not appearing in any of the previous three rounds. He was also the second goalie in the NHL expansion era (since 1968) and eighth in League history with a Cup clincher after not starting during Game 1 of the Final.

Bussi signed a one-year, entry-level contract with the Boston Bruins on March 30, 2022, after three seasons at Western Michigan University. He was named to the 2023 American Hockey League All-Rookie team after going 22-5-4 with a 2.40 GAA and .924 save percentage for Boston's affiliate in Providence. He was 46-25-5 with a 2.61 GAA and .910 save percentage in the NCAA, and 63-31-13 with a 2.61 GAA, .915 save percentage and eight shutouts in the AHL.