After serving as a Mormon missionary in Chile from 2014 to 2016, Bushman played for the BYU Cougars football team from 2017 to 2020.
[8][9][10] In October 2013, he committed to play college football and baseball for the BYU Cougars of Brigham Young University.
Bushman impressed local media with his performance at 2017 spring camp, catching four passes for 105 yards and two touchdowns in the rain during a scrimmage.
[13][12] BYU quarterback Tanner Mangum stated that "Matt has been a great addition to our team and he's worked hard to be a legitimate target for us.
[15][5] He played in all 13 games, starting eight, as a true freshman during the 2017 football season, catching 49 passes for 520 yards and three touchdowns.
[16][5] Bushman also led the NCAA Division I Football Bowl Subdivision (FBS) in receptions and receiving yards by a freshman tight end.
[5] In July 2018, Bushman was named to the watchlist for the John Mackey Award, given to college football's best tight end.
[17] He played in all 13 games, starting eight, for the second consecutive season in 2018, recording 29 receptions for 511 yards and two touchdowns while earning Phil Steele All-Independent first team honors.
[18][5] Bushman's 17.6 yards per catch was the best by an independent school player that season and also the best for any FBS tight end.
[5] Bushman became the third BYU tight end, after Gordon Hudson and Dennis Pitta, to record over 500 receiving yards for three straight years.
[25] Although he still had a year of eligibility remaining due to the COVID-19 pandemic, Bushman decided to enter the 2021 NFL draft.
[26] Afterward, Bushman began training at EXOS Physical Therapy and Sports Medicine in Scottsdale, Arizona.
[26] The Deseret News reported that Bushman looked fully recovered during BYU's pro day on March 26, 2021.
[28] Bushman was rated the 249th best prospect in the 2021 NFL draft by Scouts Inc.[29] Lance Zierlein of NFL.com stated "He has good yards-per-catch numbers and quality ball skills, but is unable to separate against tight man coverage and struggles to finish contested catches.
[33][38] After a visit, Bushman signed with the Kansas City Chiefs on January 4, 2022, joining Nakia Griffin-Stewart and Mark Vital as the third tight end on the practice squad.
[33] Bushman was re-signed to the practice squad on December 20, 2022, after injuries to Chiefs tight ends Jody Fortson and Noah Gray.
[46][47] On September 7, just hours before kickoff, Bushman was elevated to the active roster after Travis Kelce was questionable for the day's season-opening game against the Detroit Lions.
[5] He started the Matt Bushman Foundation in January 2021 in order to give underprivileged kids athletic equipment and sports opportunities.