Bradford appeared in all 12 games as a true freshman at TCU in 2019, totaling 23 tackles.[3] He then appeared in 10 games in 2020, recording 44 tackles and 6.5 tackles-for-loss (TFLs), and 11 games in 2021, eight as a starter, finishing fourth on the team with 52 tackles and 2.5 TFLs.[3] He helped the Horned Frogs reach the national championship in 2022, placing fifth on the team with 58 tackles while starting all 12 games and having eight pass breakups.[3][4] He returned for a final season in 2023, recording 54 tackles, six passes defended and two interceptions.[4] He was an honorable mention All-Big Ten Conference selection in both 2022 and 2023 and was invited to the NFL Scouting Combine at the conclusion of his collegiate career.[3][4]