Buford HS won the Georgia Class 4A State Championship his senior year going 34–2 and finishing ranked as 8th in the MaxPreps National Poll.

The Tampa Bay Rays selected Bart in the 27th round of the 2015 MLB draft, but he opted not to sign.

[15] Considered a top prospect in the 2018 MLB draft,[12][16] the San Francisco Giants selected Bart with the second overall pick.

[27] In August, the Giants promoted Bart to the Richmond Flying Squirrels of the Class AA Eastern League,[28] with whom he finished the year.

[31] With the 2020 minor league season cancelled due to the COVID-19 pandemic, the Giants assigned Bart to their alternate training site.

[39] On July 10, due to the hand injury of Buster Posey, the Giants called Bart up again after he was hitting over[clarification needed] .335 with an OPS of over .980.

[41] The following day, Bart was optioned back down to Triple-A Sacramento due to the MLB All-Star break.

[42] Bart began the 2022 season with San Francisco, and hit his first career home run off of Miami Marlins starter Sandy Alcántara on April 8.

[45] Bart made the Opening Day roster for the Giants in 2023, but ceded starting duties to Roberto Pérez to begin the year.

[46] After Pérez underwent season–ending surgery on April 13, Bart assumed the starting role, with Blake Sabol serving as the backup.

[53] Bart began competing with Henry Davis for playing time, as Jason Delay and Yasmani Grandal were injured.