Whether the student loans are private are not is, under the current law, irrelevant. When you say "file bankruptcy on" I assume you are asking whether or not the student loans are dischargeable. The answer is the same as it has been for a long time now: Student loans can only be discharged if you can prove, after trial, that repaying the loans would constitute an "undue hardship" on you as that term is defined by the courts in your jurisdiction.
You need to consult with an experienced bankruptcy attorney in your area for more details on that option, but it does require you to meet a very high burden of proof and go through a separate trial after filing a bankruptcy case, so it's not inexpensive.
Mark Markus has been practicing exclusively bankruptcy law in California since 1991. He is a Certified Specialist in Bankruptcy Law by the State Bar of California Board of Legal Specialization, AV-Rated by martindale.com, and A+ rated by the Better Business Bureau.