If I put all of my student loan debt on a credit card, could I cancel this out by declaring bankruptcy?

I would strongly advise you not to go that way. You will carry that mark against you for life. Talk to your student loan creditors and tell them that you are doing it really tough. Most will understand and help you come to a better arrangement that's suitable to you both. I have been in a similar position to you and I worked out a solution with my creditors. Maybe you could talk to a financial adviser who could show you various options. Good Luck.