Bachman attended Miami University and played college baseball for the Miami RedHawks. He joined the RedHawks' starting rotation going into his freshman season and had a 7–1 win–loss record with 3.93 earned run average (ERA) and 75 strikeouts in 75+2⁄3 innings pitched.[2] His average fastball increased during his college career from 91 to 100 miles per hour (146 to 161 km/h).[3] Bachman had an 3.42 ERA with 31 strikeouts in 23+2⁄3 innings pitched before the season was cut short due to the coronavirus pandemic.[4] Bachman was projected to be a first round selection in the 2021 Major League Baseball draft going into his junior season.[5][6][7] Bachman went 4–4 in his junior season with a 1.81 ERA and 93 strikeouts in 59+2⁄3 innings pitched and was named first team All-Mid-American Conference.[8][9]
The Los Angeles Angels selected Bachman in the first round, with the ninth overall pick, in the 2021 Major League Baseball draft.[10] On July 21, 2021, he signed with the Angels for a $3.85 million bonus.[11] Bachman was assigned to the High-ATri-City Dust Devils to start his professional career.[12] Over 14+1⁄3 innings, he went 0–2 with a 3.77 ERA and 15 strikeouts.[13]
Bachman began the 2022 season on the injured list with back spasms.[14] He was assigned to the Double-A Rocket City Trash Pandas upon being activated.[15] After missing two months with a biceps issue, Bachman ended the year making 12 starts and registering a 3.92 ERA with 30 strikeouts in 43.2 innings pitched.[16]
Bachman returned to Rocket City in 2023, making 6 starts and struggling to a 3–2 record and 5.81 ERA with 29 strikeouts in 26.1 innings pitched. On May 26, Bachman was promoted to the major leagues for the first time.[17] He made his major league debut that night against the Miami Marlins, pitching two innings in relief.[18] After 11 games for the Angels, he was placed on the injured list with right shoulder inflammation on July 14.[19] Bachman was transferred to the 60–day injured list on August 1.[20]
Bachman was placed on the 60–day injured list to begin the 2024 season as he recovered from offseason shoulder surgery.[21] He was activated from the injured list and optioned to Double–A Rocket City on June 14, 2024.[22]