Since you are asking the question here, it sounds like you are the type of person who is uncomfortable asking your friend to quiet down. If this is the case and you want to listen to music without telling her to be quiet, you could consider choosing music that she can't sing to. Instrumental, classical, foreign languages, etc. I assume if she is like most people she only sings along to the stuff she is familiar with and knows the lyrics to. If you make a mix CD or create an unusual play list on your iPod, it might allow you to hear some music without her accompaniment and while still avoiding asking her to be quiet. Other avoidance audio options include talk radio, audiobooks, podcasts, radio theater plays, etc.

I personally would have no problem asking a friend not to sing in the car while I was driving. I would find it distracting and annoying, especially if I was in heavy traffic or challenging road conditions. It would have been best to mention this when it first started, as now you have a precedent to overcome, but it still sounds worth doing if you are going to continue to commute with her. If you nicely blame it on the distraction/safety issue rather than tell her she has a voice like a braying mule, it shouldn't be much of an issue between friends. If you are the passenger in her car, it might be a bit more awkward but the friendship still shouldn't be strained from the discussion unless she is hypersensitive.