Sounds like my 330 did when the alternator pulley was shot, start cheap with the belt and then look more into pulleys if that doesn't fix it, you recently bought it so a new belt will give piece of mind and maybe fix the issue. if not the pulleys are easy to change and I will help you with it if you want
My 135i did the same thing. I had the pully and belt replaced since it was still the OEM belt at 65k miles and I wanted to get it all done without having to worry about it. But the pully was the issue so it was replaced.
Current: 2011 BMW 335xi Sedan / Alpine White / Black Leather / PPK 2 / BMW Performance Exhaust & BMW Tune / M Package / Carbon bits in a few places..