I've got a similar problem with mine which I haven't fixed yet.
I read a few topics on it around the internet and from what I can see buying an aftermarket alternator didnt fix the problem but as soon as they got a genuine BMW one it went away. Somebody recommended getting one of a breakers and replacing the voltage regulator, apparently he's fixed a couple like that.
I got a new battery for mine 2-3 months ago and it was running fine until 2 weeks ago. I haven't driven it all weekend and when I tried to start it on monday to go to work it wouldnt and the OBC readout showed less than 10V on the battery (ridiculous). Anyway I charged the battery and when I started the car the alternator voltage readout was showing less than 13v!
How do i know it's the alternator though? Could it be a faulty part/wire that's eating up the voltage? I've also been having bad idling and errors about the O2 sensor and thermostat (O2 sensor has been changed), was wondering whether this can have anything to do with it.
Anyway let us know how you get on...