Bradshaw was a consensus five-star recruit and one of the top players in the 2023 class, according to major recruiting services.[6][7] On October 14, 2022, he committed to playing college basketball for Kentucky over offers from Louisville, Texas, UCLA and USC.[8][9] Bradshaw also considered playing professionally in the NBA G League.[10]
Bradshaw enrolled at the University of Kentucky in June 2023.[11] Shortly after enrolling, he underwent surgery on a broken foot that caused him to miss all of the Wildcats' preseason training and the start of his freshman season.[12] Bradshaw was cleared to play one month into the season and made his college debut on December 2, 2023, in the Wildcats' upset loss to UNC Wilmington.[13] The following game, he scored a season-high 17 points with 11 rebounds, three blocks, and one steal as Kentucky beat Penn 81-66.[14] Bradshaw became the Wildcats' starting center afterwards, but was moved back to the bench at the end of January.[15] He finished the season averaging 4.9 points and 3.3 rebounds over 26 games played.[16] Bradshaw announced he would be entering the NCAA transfer portal shortly after it was reported that Kentucky head coach John Calipari would be leaving the program to become the head coach at Arkansas.[17]
On April 15, 2024, Bradshaw announced on his Instagram page that he would be committing to Ohio State.[18]