[2] Bush was selected in the 40th round of the 2018 Major League Baseball draft by the Kansas City Royals, but opted not to sign with the team.
[3] Bush began his collegiate career at Washington State, where he pitched in 19 games as a freshman and finished the season with 0-5 record with a 12.69 ERA.
[4] Bush transferred to Saint Mary's College and was named first team All-West Coast Conference as a junior after posting a 7-5 record with a 2.99 ERA in 14 starts.
[11] On July 26, 2023, Bush and Edgar Quero were traded to the Chicago White Sox in exchange for Lucas Giolito and Reynaldo López.
On February 11, 2025, general manager Chris Getz announced that Bush would undergo Tommy John surgery and miss the entirety of the 2025 season.