This may sound like a really silly question, but I am wondering how much out of pocket expense I would likely have as a person with no health insurance, birthing in a private hospital? Or is this even possible?

We really really want a vba3c and the only hospital around here where I would have a chance at having one is a private hospital. Someone mentioned to me about just going there anyway and paying the expenses. Does anyone know roughly how much out of pocket this would be?? $5000, $10000, $30000? I have NO idea...