This thread's almost a month old, so I don't know if you found a solution yet. However, I have; I have a Galaxy Nexus as well and while I love to be on the leading (and sometimes bleeding) edge of technology, that whole "MTP" thing really annoyed me.
Anyway, I have a late 2011 135i and got the same problem; my Nexus comes up on my display as "Galaxy Nexus" but doesn't really work. I think the MTP implementation in the Nexus is either not complete or the MTP support in iDrive just isn't there. I have no way of testing other methods.
So rather than try to fix the car (difficult and time consuming), I fixed the Nexus. Get thee to XDA Developers and thou shalt find
http://forum.xda-developers.com/show....php?t=1389375 where there's a lovely little app that basically puts USB Mass Storage support back. Works like a champ on my Jelly Bean equipped Nexus.
As a side note, I really hate the fact that BMW is so great on support for iOS, but not Android devices.