Bauer is from South Western Sydney. Bauer's junior football was played with the Under 12s with the Wollondilly Redbacks until U12s, U17 with the Western Suburbs and Inner West Magpies in the Sydney AFL. Bauer was a member of the Sydney Swans Academy.[2] After going undrafted in the AFL national draft, he began the 2022 season playing for North Adelaide in the SANFL. He was then drafted by Richmond with the club's first pick and the 10th selection overall in the 2022 mid-season draft.[3]
Bauer played the next year for the Richmond reserves, notably kicking after-the-siren game winning goals in two separate matches during June 2023.[4] He made his senior debut for Richmond in round 17 of the 2023 season, but suffered a match-ending hamstring injury less than two minutes into the game substituted of.[5] After rehabilitating, he returned the senior team in round 21.[6]