Bowman entered his freshman year at Texas Tech in 2018 in a three-way battle for the starting position against junior McLane Carter and sophomore
Jett Duffey, with Carter being named the starter for the week 1 game against
Ole Miss.[5] Bowman entered the game in the 2nd quarter after Carter suffered a high ankle sprain. Bowman went 29/49 for 273 yards with a touchdown in the 27–47 loss.[6] Bowman was named the starter for the week 2 match-up against
Lamar, completing 22-of-25 passes for 282 yards with 2 touchdowns, only playing the first half of the game.[7] A week later on September 15, Bowman had a historic game against
Houston, completing 43-of-59 passes for 605 yards with five touchdowns in the 63–49 win. Bowman's 605 yards set a
Big 12 record for most passing yards in a game by a freshman.[8] On September 29 against
West Virginia, Bowman left the game right before halftime after being sandwiched between two defenders with an apparent upper-body injury; it was later revealed that Bowman had suffered a partially
collapsed lung.[9][10] Bowman returned from injury on October 20 for the Red Raiders' game against
Kansas; Bowman finished 36/46 for 408 yards with three touchdowns and an interception.[11][12] On November 3 against
Oklahoma, Bowman left the game at halftime for an unknown reason. It was later revealed that he had a re-occurrence of a partially collapsed lung; Bowman was discharged from the hospital on November 7.[13][14] Bowman finished his freshman year with 227 completions out of 327 attempts for 2,638 yards with 17 touchdowns and 7 interceptions.
Bowman started in Texas Tech's first game of the 2019 season against
Montana State, his first game since November 3, 2018. Bowman played most of the game, completing 40 passes out of 53 attempts for 436 yards with two touchdowns along with a rushing touchdown in the 45–10 victory.[15] On September 14 Bowman suffered a shoulder injury against
Arizona and was expected to be out for several weeks.[16] Bowman
redshirted on November 11 after being cleared to play again.[17]
In the third game of the 2020 season Bowman left during the 1st quarter against
Kansas State with an apparent leg injury; Bowman finished the game 4-of-7 for 23 yards.[18][19] Bowman returned from injury and started the next game against no. 24
Iowa State.[20] Bowman struggled in the game and was benched in favor of
Utah State transfer
Henry Colombi, who was later named the team's starter moving forward.[21] On November 14 against
Baylor, Bowman played one series that ended with him throwing a
pick six. Bowman would enter the game again in the 3rd quarter after Colombi suffered an injury to his non-throwing arm; the Red Raiders were down 6–20 when Bowman entered. Bowman would lead Texas Tech back in the game, leading the team on three scoring drives in the second half that resulted in a 24–23 victory for the Red Raiders.[22]
Michigan
On February 28, 2021, Bowman announced that he would be transferring to
Michigan for the upcoming season.[23] Prior to the
2021 season, redshirt sophomore
Cade McNamara was named Michigan's starting quarterback, beating out Bowman and five-star freshman
J. J. McCarthy.[24] Bowman appeared in the team's game against
Wisconsin, the fourth quarterback Michigan used in the game, throwing an interception.[25]