He learned to play ice hockey through his father alongside his brother Ty and cousins Ella and Mitchell Vande Sompel.

[5] As he was reluctant to join the OHL and give up his NCAA eligibility, Bryson competed with the Neponset Valley River Rats U18 team where he scored 12 points in 14 games.

During his time at Loomis, Bryson helped the Pelicans win the Founders League and the Avon Old Farms Hockey Christmas Classic and reach their first-ever Stuart/Corkery Elite Eight Tournament.

By November 2015, the Lancers held a 9–6–2 record while Bryson was tied for second among USHL defencemen in scoring with one goal and 11 assists through their first 17 games.

[8] By January, Bryson led all rookie defensemen in scoring with 19 points and earned an invite to compete at the 2016 USHL/NHL Top Prospects Game.

[10] Following his freshman season, Bryson was named to the Hockey East Association's All-Academic Team for achieving a grade point average of 3.0 or better.

[19] The following month, Bryson tallied career-highs in goals, assists, and points and received the Hockey East's Len Ceglarski Award.

[20] Throughout the month of April, the Friars attempted to qualify for the 2018 NCAA Division I men's ice hockey tournament but fell 2–1 in a quarterfinal matchup against Notre Dame.

Upon stepping into this new role, he began the season tallying 14 points through the teams' first 13 games to tie for ninth among NCAA defensemen.

[24] Bryson finished the regular season with four goals and 24 assists through 42 games to earn a second nomination to the Hockey East's Second All-Star Team.

[25] As the team qualified for the 2019 NCAA Division I men's ice hockey tournament, he helped the Friars record six unanswered goals against the Minnesota State Mavericks to lift them to the Regional Finals against the Cornell Big Red.

[25] While facing off against the University of Minnesota-Duluth Bulldogs in the Frozen Four, Bryson tallied an assist on the Friars' only goal of the game as they fell 4–1.

[38] Upon re-joining the team, Bryson again earned praise from the Sabres' head coach who said he was pleased with the defenceman's puck management, poise, and mobility.