It would be both of them, really.
Right now, under US law, you can't declare bankruptcy from student loans. A bailout would imply changing that rule so that we can let people with student debt off of their obligations.
You'd also, natch, be bailing out the people who hold this debt.
I'm really not sure what the path forward is, here. Theoretically, the most important line of defense against a bad loan being made is that the lender doesn't want to lose money, and therefore won't make a bad loan in the first place. This isn't always awesome on its face, because it means that people don't get to buy things they don't have the money for right now. But it's really kind of nice. It also protects people from taking on debts they can't afford, because that translates into default risk. And it protects people from taking on debt to buy things that are overpriced, because that translates into collateral risk.
But at some point we decided that being able to get certain kinds of loans (mortgages and student loans) is very nearly a natural right, because they give access to things that we associate with prosperity (land ownership and a postsecondary education). So then the government sets up programs to greatly reduce the barriers to access to these kinds of loans, by essentially setting up a whole bunch of special rules and programs that make it easy for lenders to ignore default risk. And if you don't care about default risk, you'll make much bigger loans than you would otherwise, which fuels prices getting out of control.
We saw how that went down with housing. Now we're going to see how that goes down with student loans. I'm not sure there are any good answers there. Personally, I like the idea of leaving lenders to sink or swim. They've had a nice long ride on a gravy train fueled by government largesse, and, if they failed to contingency plan for the possibility that someone might turn off the gravy spout, I don't feel particularly bad about that. But the lenders are financial institutions, and, as we've seen, the financial industry is such a horrible tangle that it's hard to anticipate the ultimate repercussions of letting them fail.
But it's also hard to anticipate the repercussions of a bailout - money doesn't grown on trees, so the funds used to make the bailout need to come from somewhere. When it comes to government intervention on this sort of thing, though, I'm kind of inclined to take my mother's advice: "It'll never heal if you don't stop picking at it."