He previously played for the Colorado Avalanche of the NHL and has appeared with the Canada men's national ice hockey team in international competition.

The son of NHL player Shawn Byram, Bowen was coached by his father until the age of 12, when he began playing full-time minor ice hockey in Alberta.

[8] Playing his first full season with the Giants in 2017–18, Byram scored his first WHL goal on October 21, 2017, as part of a 5–2 victory over the Regina Pats.

[9] By February, Byram was registering almost 23 minutes of ice time per game, and was considered not only a top prospect for the National Hockey League (NHL) but a future captain for the Giants.

[12] Although the Giants lost their opening-round playoff series to the Victoria Royals, Byram added three postseason goals and four assists to his season totals.

[17] After a five-point game against the Kamloops Blazers on January 13, 2019, Byram, who set a franchise record for most single-game points by a defenceman, was named the WHL On the Run Player of the Week.

[26] He had a slow start with Vancouver that season, netting only three goals in 27 games before leaving the team to join Canada at the 2020 World Junior Ice Hockey Championships in December.

[30] As he had participated abroad in the 2021 World Junior Ice Hockey Championships, Byram's NHL debut was delayed as he had to clear a seven-day quarantine and produce four negative COVID-19 tests before joining his teammates in Colorado.

[31] He made his NHL debut on January 21, 2021, playing for 11 minutes with one shot on goal and one minor penalty in a 4–2 loss to the Los Angeles Kings.

[46][47] Playing beside veteran defenceman Erik Johnson,[48] Byram was a break-out player for the Avalanche during the 2022 Stanley Cup playoffs, taking on a greater responsibility on defence when Sam Girard suffered a broken sternum during Colorado's second-round series against the St. Louis Blues.

[49] Byram recorded nine assists in 20 playoff games as the Colorado Avalanche were NHL champions, defeating the Tampa Bay Lightning in the 2022 Stanley Cup Finals.

[53] Upon his return, Byram took a more active approach on offence, leading to 18 points in his first 28 games back, including a three-game goal streak at the end of March.

[59] Byram missed eight games in January with a lower-body injury, which he took as an opportunity to "sit back and watch for a bit" and reset his uneven season.

[60] Paired at times with Girard, Cale Makar, Josh Manson, and Jack Johnson, Byram recorded eight goals and 20 points in 55 games that season with Colorado.

[63] Sabres general manager Kevyn Adams had spent considerable time looking for a young, top-rated defenceman, and when Colorado acquired Sean Walker from the Philadelphia Flyers, they were willing to move Byram.

[65] The trade reunited Byram with childhood friends Dylan Cozens and Peyton Krebs, and he referred to the new environment as "a breath of fresh air".

[76] With Buffalo not qualifying for the 2024 Stanley Cup playoffs,[77] Byram was one of three Sabres players to represent the Canada men's national ice hockey team at the 2024 IIHF World Championship in Czechia.

[78] Byram recorded one goal and five points in nine games as Canada finished in fourth place, falling 4–2 to the Swedish national team in the bronze-medal match.