Alright, I don't know if that code is rich or lean.
But if it us just one bank it has to be something that effects only the one side. So fuel pressure and anything in the intake before the throttle is out.
You have tried a number of things. My next step would be checking the fuel injectors, if it was me at least.
But if it is at the dealer, why are they giving you generic obd codes not BMW specific codes?