One of the things I decided never to have a problem with, and never hesitate to do, is talk money with my clients. They realize you charge for your services. They understand they are hiring you, a professional.
So, I just matter of factly state, "OK, to book the date, 50% up-front is required. Otherwise the date is not confirmed. The other 50% is due at the beginning of the the session after the first 50% is used up. For instance, if it's a two-day session, I need the first day now, and payment for the second day is due at the beginning of the second day. If it's only a one-day session, the terms are pre-payment in-full. "
Say it confidently and with a smile. If they really want you and value you, they will pay the money on your terms. If they can't, well, I guess they couldn't have afforded you anyway, right? They would have been more trouble than they're worth.
When I give my terms openly and unashamedly, the client almost always says, "Great. I can write you a check today."