[citation needed] The San Diego Padres selected Bush first overall in the 2004 Major League Baseball draft, originally as a shortstop.

[5] His fastball reached a speed of 98 miles per hour (158 km/h), and he had prior knowledge of pitching from his days as a high school ace.

After a promising start in rookie league, Bush tore a ligament in his pitching elbow in August 2007, ending his season.

[7] Shortly afterward, it was learned that Bush was allegedly intoxicated in a high school parking lot where he assaulted two freshman lacrosse players.

He played one injury-plagued season for the Single-A Charlotte Stone Crabs in the Florida State League before being added to the Rays' 40-man roster in November.

[12] During the 2011 season, Bush played for the Rays' Double-A affiliate, the Montgomery Biscuits of the Southern League, primarily as a late reliever and occasional closer.

On April 7, 2016, Bush threw his first professional pitch in almost five years for the Frisco RoughRiders of the Double-A Texas League, as he earned a save in one inning, while allowing one hit.

[16] He worked the ninth inning against the Toronto Blue Jays that night, retiring the heart of the Jays lineup (Josh Donaldson, José Bautista, and Edwin Encarnación) by inducing a double-play off the bat of Edwin Encarnación after hitting José Bautista with a pitch.

On May 15, Bush earned his first major league win in a 7–6 victory over the Toronto Blue Jays, a game more noted for the scuffle between Rougned Odor and José Bautista that would wind up in a bench-clearing brawl.

However, he was demoted to the Triple-A Round Rock Express on April 25 to work on his command as he had walked nine batters in 11+1⁄3 innings pitched along with posting a 1.50 WHIP.

[19] Bush underwent surgery on his right elbow to fix a partial tear of his ulnar collateral ligament (UCL) in September 2018.

[22] On July 3, the Rangers announced that Bush suffered a torn UCL and would undergo a second Tommy John surgery; ending his 2019 season.

On August 1, 2022, Bush was traded to the Milwaukee Brewers in exchange for infielder Mark Mathias and pitcher Antoine Kelly.

[35] A few weeks after the Padres drafted him in 2004, Bush was arrested on suspicion of felony assault, misdemeanor trespass, disorderly conduct, and underage drinking, after he allegedly fought with security trying to escort him out of a bar.

[36] In early 2009, Bush was allegedly involved in a drunken assault at a San Diego high school, which was caught on camera.

This led the Padres to designate Bush for assignment following the team's signing of Cliff Floyd and then trade him to the Blue Jays.

[3][8] Only a month later, he assaulted and berated a woman at a party in Florida, and was released by the Blue Jays for violating a "zero tolerance" agreement.

In the incident, Bush hit 72-year-old motorcyclist Tony Tufano on the Tamiami Trail (U.S. Route 41) northbound in Port Charlotte, Florida, running over his head as he fled the scene in a Dodge Durango belonging to teammate Brandon Guyer.

Bush remains a suspect in two other hit and run accidents further north on the Tamiami Trail in Venice that occurred earlier that day.

[39] The Rays placed Bush on the restricted list for the 2012 season, meaning that he was no longer on the 40-man roster, nor did he accumulate service time.

On December 18, 2012, Bush accepted a plea bargain and pleaded no contest to one count of DUI with great bodily injury.