[vilord]

Another option is to go to car-part.com, search for a 2011 bmw 328i -> computer box (not engine), then "Communication, (Bluetooth)".

I see some for as little as 40 bucks.

If you find one for a 2011/2012, it's at least a 30% chance of being the right part. Could also be entirely wrong.
You could email or call whatever parts yard and ask for a picture of it and/or the part number.

If you look at my photo ^^ you can see that next to the antenna connections, there's a slot in the baseplate near where the mounting screws are. All combox models look like this. TCU does not look like this, nor does MULF or sirius/xm or whatever else the parts yard might "think" is a bluetooth module.