During the summer of 2008, Bjugstad turned down an invitation to train with the USA Hockey National Team Development Program out of a sense of loyalty to his high school teammates.

[1] Bjugstad began his collegiate career at the University of Minnesota in 2010 playing for the Golden Gophers, where he totaled 54 goals and 44 assists during his three years while the team won two WCHA championships.

Bjugstad left the Gophers after his junior season, signing a three-year entry-level deal with the Florida Panthers on April 3, 2013.

Bjugstad rebounded from his disappointing previous season by setting career highs in points, assists, and games played during his 2017–18 campaign.

As a pending unrestricted free agent, Bjugstad opted to remain with the Wild in signing a one-year, $900,000 contract extension on July 5, 2021.

[22][23] Bjugstad made an immediate impact to the Oilers bottom six forward group, contributing with 4 goals and 6 points through 19 regular season games.

He collected a career best three postseason goals through 12 playoff games, before the Oilers were defeated in the second round to the eventual Stanley Cup Champions, the Vegas Golden Knights.

As a free agent from the Oilers, Bjugstad opted to return to former club, the Arizona Coyotes, in agreeing to a two-year, $4.2 million contract on July 1, 2023.