Bronson began his college career at Temple and redshirted his true freshman season after breaking his ankle in training camp.[1] He did not play in any games as a redshirt freshman and transferred to Washington at the end of the season following the departure of Temple head coach Matt Rhule.[2]
Bronson joined the Washington Huskies as a walk-on and did not see any playing time in his first season with the team. As a redshirt junior, he played in 12 games and had 11 tackles with one tackle for loss and one sack. Bronson was awarded a scholarship during spring practice after the season.[3] He became a starter during his redshirt senior season and finished the year with 23 tackles, four tackles for loss, and two sacks. Bronson was granted a sixth season of eligibility by the NCAA for the 2020 season.[2]
Bronson was signed by the New Orleans Saints as an undrafted free agent on May 2, 2021.[5] He was waived during final roster cuts on August 31, 2021, but was signed to the team's practice squad the next day.[6] Bronson was elevated to the active roster on October 26, 2021, for the team's week 7 game against the Seattle Seahawks and made his NFL debut in the game.[7] He was signed to the Saints' active roster on November 20, 2021.[8] He was waived on December 14, 2021.
Cleveland Browns
Bronson was claimed off waivers by Cleveland Browns on December 15, 2021.[9] Bronson was waived by the Browns on December 30, 2021.[10]
Dallas Cowboys
On January 5, 2022, Bronson was signed to the Dallas Cowboys practice squad. He signed a futures contract on January 19. He was waived on August 30, 2022.[11]
Miami Dolphins
On September 5, 2022, Bronson signed with the practice squad of the Miami Dolphins.[12] He signed a reserve/future contract on January 16, 2023.[13] He was waived on August 28, 2023.[14]