This is not at all your fault. You should not feel guilty about a thing. That vet is the one to blame. I mean, you even asked if he wanted to do xrays. HELLO!! And with the mistake or oversight on his part he'd better let you work out a payment plan. Had he taken xrays two months ago it may not have gotten to this point. I mean, she probably still would have had to have surgery, but it wouldn't have been such a dire emergency and last minute type of thing.
Oh, I am just so sorry you and Henny had to go through all of this. I hope she is home with you very soon and on a quick road to recovery.