After graduating from Shattuck, Bļugers spent four seasons at Minnesota State where he earned All-Tournament Team honors.

Although he only played for part of the playoffs, Bļugers would win the Stanley Cup with the Golden Knights that season, and sign with the Canucks the following off-season.

[6] Due to his father's career as an attorney and a member of the Latvian Ice Hockey Federation, Bļugers attended the International School of Latvia before leaving for Shattuck-Saint Mary's in Faribault, Minnesota.

[18] Bļugers was traded to the Vegas Golden Knights on 1 March 2023, in exchange for a third-round pick in 2024 and prospect Peter DiLiberatore.

[21] When the Golden Knights faced off against the Dallas Stars in the Western Conference finals of the 2023 Stanley Cup playoffs, Bļugers scored his first goal of the postseason in Game 1.

[25] On 1 July 2023, Bļugers left the Golden Knights as a free agent and was signed to a one-year, $1.9 million deal with the Vancouver Canucks for the 2023–24 season.

[26] On June 26, 2024, Bļugers agreed to terms on a two-year contract with the Canucks worth $1.8 million in average annual value.