He spent five seasons at Letzigrund making over 100 appearances for Grasshoppers before joining Russian Premier League club Rubin Kazan June 2016.

Bauer began playing football with the youth teams at SC Veltheim, Grasshopper Club Zürich and FC Winterthur.

[4] A youth exponent from Grasshopper Club Zürich, Bauer made his Swiss Super League debut on 14 August 2011 against BSC Young Boys playing the full game which ended in a 3–0 defeat.

[19][20] Bauer made his Celtic debut in a 2–0 Old Firm victory over Rangers at Ibrox on 1 September 2019 where he was on the receiving end of a strong tackle from Jordan Jones who was sent-off.

[22] He played 13 matches for Celtic as they won a ninth consecutive Scottish Premiership title as the season was ended early in May 2020 due to the COVID-19 pandemic.

[23] On his return to Stoke, Bauer was left out of the first team by Michael O'Neill and was loaned to Russian side FC Ufa in February 2021.