Bader attended the Horace Mann School in the Riverdale neighborhood of The Bronx, New York City, and played for the school's baseball team. While attending high school, Bader also played for the New York Grays, a club baseball team. In October 2011, Bader committed to the University of Pittsburgh to play for the Panthers baseball team. However, he had not signed a National Letter of Intent and decommitted from Pittsburgh in May 2012, and committed to the University of Maryland to play for the Terrapins. However, Maryland did not offer him a scholarship. In July, he decommitted from Maryland, and committed to the University of Florida to play for the Gators, as Florida offered him a partial scholarship. Bader led the Gators with a.312 batting average as a freshman and with a.337 average as a sophomore. In 2014, his sophomore year, Bader was suspended for 19 games after a scooter accident that occurred while he was driving under the influence of alcohol. After the 2014 season, he played collegiate summer baseball with the Bourne Braves of the Cape Cod Baseball League. As a junior in 2015, he batted.297 with 17 home runs and 66 RBIs in 67 games. He was named to the All-Tournament Team in the 2015 College World Series after he batted.348 in five games.
Professional career
In the 2015 Major League Baseball draft, the St. Louis Cardinals selected Bader in the third round, with the 100th overall selection. He signed with the Cardinals, receiving a $400,000 signing bonus, and made his professional debut with the State College Spikes of the Class A-Short SeasonNew York–Penn League, hitting two home runs in his first game. The Cardinals promoted Bader to the Peoria Chiefs of the Class AMidwest League in July. He was the MWL Player of the Week for August 24–30 after batting.448 in seven games with two home runs, six RBIs, one double, and two triples. In 61 total games between State College and Peoria, he batted.311/.368/.523 with 11 home runs, 32 RBIs, 13 doubles, and 17 stolen bases. Bader began the 2016 season with the Springfield Cardinals of the Class AATexas League. He had a hit streak in April 2016 that fell one game short of tying the Springfield club record. Bader was named an outfielder in the Texas League mid-season All-Star Game, in which he collected four hits in five at-bats with a double and a run scored. He was promoted to the Class AAAMemphis Redbirds on July 6, 2016. In their updated 2016 mid-season ranking, Baseball America rated Bader in the top 100 for the first time, at 89th. Bader finished the 2016 season batting a combined.267 with 19 home runs and 58 RBIs in 131 games between Memphis and Springfield. MLB Pipeline named him the Cardinals 2016 Minor League Player of the Year. After the season, the Cardinals assigned Bader to the Glendale Desert Dogs of the Arizona Fall League. Bader began 2017 back with Memphis. On July 25, 2017, the Cardinals promoted Bader to the major leagues to take the place of the injured Dexter Fowler. Bader had been batting.297 with 19 home runs and 48 RBIs in 97 games at Memphis before his promotion. That night, he started in center field and batted seventh, and recorded his first major league hit, a double, and scored the winning run on a walk-off sacrifice fly. He hit his first MLB home run, a 395-foot shot to left field, on September 1, 2017, off Johnny Cueto, leading the Cardinals to an 11-6 win over the San Francisco Giants at AT&T Park. After the season, the Cardinals named Bader their 2017 Minor League Player of the Year. MLB.com ranked Bader as St Louis' fifth-best prospect going into the 2018 season, which he began with Memphis. The Cardinals promoted him to the major leagues on April 3 after an injury to Jedd Gyorko. After his call-up, Bader became St. Louis' fourth outfielder, then their starting center fielder after Tommy Pham was traded on July 31, 2018. Bader finished his 2018 rookie campaign batting.264 with 12 home runs, 37 RBIs, and 15 stolen bases in 138 games; he ranked fourth among MLB outfielders with 19 Defensive Runs Saved. Bader began 2019 as St. Louis' starting center fielder. However, he was eventually moved into a bench role due to offensive struggles, and was ultimately demoted to Memphis on July 30. At the time of his demotion, he was slashing.195/.309/.648 with six home runs and 19 RBIs over ninety games. He was recalled to St. Louis on August 20. In his first game after being called back up, Bader hit a triple, scored two runs and walked three times in a 9–4 win over the Milwaukee Brewers. Bader finished the 2019 regular season with St. Louis, batting.205/.314/.680 with 12 home runs, 39 RBIs, and 11 stolen bases over 128 games. Following the season, he was nominated for his first ever Gold Glove.