I keep getting a bank 1 sensor 1 stuck rich code. What is the most likely source

Hello, it's really impossible to say without performing some hands on testing. My initial thought is - do you have a stuck open fuel injector, allowing fuel into a cylinder on bank one alone, causing an fuel delivery that is not commanded? I'm not a BMW expert, though, so maybe someone else can weigh in. Or, better yet, seek hands on guidance from a shop near you: www.repairpal.com/repair-shops