duke944 has made a good point in his very first post.
I would pay for parts but I wouldn't pay them a dime for labor. I'd love to see a training and performance history on the mechanic that worked on your bike.
Originally Posted by duke944
I'm completely confused about why you think you owe this dealer anything. If you haven't paid the bill in full, don't give them any more. If you paid by credit card dispute the charges asap. Not only did they not fix the problem, they didn't even earn a diagnostic fee for telling you what the problem is. You aren't approaching BMW correctly - call them and lodge a complaint against the dealer, of course they aren't going to help with the bill because the bike is out of warranty.