Bauer is a youth exponent from Grasshopper Club Zürich. He made his Swiss Super League debut at 14 August 2011 against BSC Young Boys. He played the full game, which ended in a 0-3 defeat.
Bauer was born in Switzerland, and has Austrian citizenship through his Austrian father. He is eligble for the Swiss and Austrian football team. Bauer got his first call up to the senior Austria side for 2018 FIFA World Cup qualifiers against Wales and Georgia in September 2017.