He made his professional debut in the 2016–17 season, appearing scoreless in five Swedish Hockey League (SHL) games.

At the conclusion of the 2018–19 season, Bemström was also named junior player of the year by the Swedish ice hockey journalist association.

[6] Bemström made the Blue Jackets out of training camp and was expected to help cover for the loss of Artemi Panarin in the offseason.

[9] In 16 games with HIFK, Bemström displayed his offensive acumen in compiling 8 goals and 17 points before returning to the Blue Jackets organization for training camp.

[11] He began the 2022–23 season assigned to Columbus' American Hockey League (AHL) affiliate, the Cleveland Monsters.

[17] Bemström scored on his debut with the Penguins, notching a power play marker in a 7–6 victory over the Philadelphia Flyers on 25 February 2024.

He failed to make Pittsburgh's roster for the 2024–25 season and after going unclaimed on waivers, was assigned to their AHL affiliate, the Wilkes-Barre/Scranton Penguins.

[20][21] Bemström played for Sweden's junior team at the Ivan Hlinka Memorial Tournament in August 2016.