Lily, you have figurative balls for posting this here, where the idea of a deposit is out of the ordinary, and not in the D&T forum, where deposits are de rigeur. I'm surprised you haven't received more vehement responses.
My opinion on deposits:
If the lady you want to see requires one, and you trust her/her reputation enough to comply and can afford to lose the deposit if you have to cancel/she flakes and never refunds it, go for it. If you don't trust her/her reputation/can't stand the thought of that money disappearing for good ... don't. Pretty simple.
I would be very wary of setting up a P.O. box to accept deposits, even a private one, and even under a business name. It's fairly easy for someone with spare time and money to find out the legal name and address of the person who owns it (unless you're 100% comfortable with clients knowing that). And Paypal is insane about not allowing any "adult" businesses to use their services. Green Dot is the best option I've found. It's not without its own issues, but it's better than any alternatives I know of.