Bemström played as a youth within the Leksands IF organization. He made his professional debut in the 2016–17 season, appearing scoreless in five Swedish Hockey League (SHL) games. However, during the season he suffered an inflammation of the pericardium and was forced out of the lineup for two months.[1] Following relegation to the HockeyAllsvenskan for the 2017–18 season, Bemström notched 8 goals and 15 points in 33 games for Leksands IF.[2] He scored his first goal in the Allsvenskan in a 3–1 win over IK Oskarshamn in October 2017.[1] Bemström left the club in the off-season and returned to the SHL by agreeing to a two-year contract with Djurgårdens IF on 2 May 2018.[2]
In the 2018–19 season, Bemström scored his first SHL goal in the first game of the season against Frölunda HC on 15 September 2018.[3] In a breakout season with Djurgårdens, he led the league in goals and power play goals and captured Rookie of the Year honours and also won the scoring title for the 2018–19 regular season with 23 goals. At the conclusion of the 2018–19 season, Bemström was also named junior player of the year by the Swedish ice hockey journalist association.[4] Djurgårdens also made it to the championship round in the playoffs, led by Bemstrom who had five goals and ten points.[5]
North America
Bemström was selected by the Columbus Blue Jackets of the National Hockey League (NHL) in the fourth round, 117th overall, of the 2017 NHL entry draft.[5] On 15 May 2019, Bemström was signed by the Blue Jackets to a three-year, entry-level contract.[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.[7] He finished his rookie season scoring ten goals and 20 points in 56 games.[8]
With the following 2020–21 NHL season delayed due to the COVID-19 pandemic, Bemström opted to continue playing in Europe after accepting a loan assignment from the Blue Jackets to play with Finnish club, HIFK of the Liiga, on 8 September 2020.[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.[10] Upon his return, his play struggled and he scored only three goals that season.[11] All three goals came in Bemström's first career NHL hat trick against Juuse Saros and the Nashville Predators on 3 May 2021.[12]
During the 2021–22 season, Bemström suffered an oblique strain in training camp and continued to struggle upon his return. He finished the season with six goals and 11 points in 41 games in the shortened season. In the offseason, Bemström signed a two-year contract extension with the Blue Jackets on 3 August 2022.[11] He began the 2022–23 season assigned to Columbus' American Hockey League (AHL) affiliate, the Cleveland Monsters. He led the league in scoring before being recalled by the Blue Jackets on 7 November. Despite playing on the top two lines, he continued to struggle and was eventually shifted down the lineup to the bottom lines before being sent back to Cleveland on 25 November.[13] He was recalled again on 28 December on an emergency basis replacing an ill Patrick Laine.[14] He remained with the team and scored a career-high 22 points in 55 games with the Blue Jackets.[15] Bemström began the 2023–24 season with the Blue Jackets, appearing in 12 games, scoring three goals and four points. However, on 15 November 2023, he was placed on waivers.[16] He went unclaimed and on 16 November, he was assigned to Cleveland.[10]
Unable to cement a full-time role within the Blue Jackets forward group, Bemström was traded to the Pittsburgh Penguins in exchange for forward Alexander Nylander and a conditional 2026 sixth-round pick on 23 February 2024.[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.[18][19] He appeared in 24 games with Pittsburgh, scoring three goals and five points. 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]