"bailout" is a fairly fuzzy term. If the banking system was working, there would have been no need for DOE loans. There was also the benefit of improved milage, thereby reducing carbon emissions. This seems like the sort of thing the DOE does anyway, and wouldn't raise eyebrows in a sane banking environment. I think by your meaning of "bailout" student loans are also a bailout.
On the other hand, GM and Chrysler went bankrupt. They sold secured assets to new GM and new Chrysler and, i believe, gave investors quite a haircut.