He played shortstop in the Eastchester Little League as a youth, with his father continuing to throw him batting practice every evening.

[14][20][21][22] 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.

[30] In 235 at-bats and 61 total games between State College and Peoria, he batted .311/.368/.523 with 13 doubles, 11 home runs, 32 RBIs, and 17 stolen bases.

[35] Bader was named a Texas League mid-season All-Star,[36] and in the All Star Game he collected four hits in five at-bats with a double and a run scored.

[38][39] Bader finished the 2016 season batting a combined .267 with 19 home runs and 58 RBIs in 465 at-bats over 131 games between Memphis and Springfield.

[46] 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 against the Colorado Rockies.

[47] 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.

[52] After his call-up, Bader first became St. Louis' fourth outfielder, then their starting center fielder after Tommy Pham was traded on July 31.

[53][54] He scored from second base on an infield single by Austin Gomber at Colorado on August 26; at the end of the season, he was the Cardinals' MLBPAA Heart & Hustle Award nominee.

[62] 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.

[63] Bader finished the 2019 regular season with St. Louis, batting .205/.314/.366 with 12 home runs, 39 RBIs, 11 stolen bases, and 13 hit by pitches over 128 games.

[64] He was one of eight major league players to record double-digit totals in home runs, stolen bases, and hit by pitches.

[10] He was named the "Best Defensive Outfielder" in the National League in Baseball America's 2019 Best Tools survey of managers, coaches, scouts, and executives.

[66] Bader returned as the starting center fielder in the COVID-19 pandemic-shortened 2020 season, slashing .226/.336/.443 with two triples (10th in the NL), four home runs, and 11 RBIs over 50 games.

[70][71] Reactivated and returned to the starting lineup on July 1, he hit his first career grand slam, helping the Cardinals to a 9–3 win over the Rockies at Coors Field.

[10][74] In October 2021, Will Leitch wrote for MLB: "Bader is a defensive dynamo, a base-running terror and a complete joy to watch.

"[75] Bader finished the 2021 season with 367 at-bats over 103 games, slashing .267/.324/.460 with 16 home runs, 50 RBIs, 21 doubles, nine stolen bases, and 6 intentional walks (8th in the NL).

[77] On defense, Bader's .973 zone rating was the highest by any Major League outfielder in history since the category began being tracked in 1987.

[81] At the time of his trade he was batting .256/.303/.370 with five home runs in 246 at-bats, with 15 stolen bases (fifth in the NL) in 17 attempts, and had been error-less in center field.

[82][55] On August 2, 2022, the Cardinals traded Bader and a player to be named later for cash considerations to the New York Yankees for pitcher Jordan Montgomery.

[84] Bader hit his first New York Yankees home run in Game 1 of the 2022 American League Division Series off of Cal Quantrill of the Cleveland Guardians.

He hit three home runs in the first four games of the series, joining Bernie Williams and Mickey Mantle as the only Yankee center fielders with three homers in a single postseason.

[88] Though Bader committed to play for Team Israel in the 2023 World Baseball Classic, he withdrew from the tournament due to a left oblique muscle injury that he suffered early in spring training.

He continued his hot streak against the Tampa Bay Rays, which included two home runs and 7 RBIs in 11 plate appearances.

[94] He missed the last two weeks of the season with a sports hernia and right adductor muscle strain that resulted in surgery on September 29.

[98] On February 7, 2025, Bader signed a one-year, $6.25 million contract with the Minnesota Twins including a mutual option for 2026.