I've required 25%-50% deposits when touring for over 10 years, and have never had an issue with people providing it. I also require similar deposits locally for my specialty packages, meetings longer than 4 hours, and any meeting with fetish or domination elements.
It weeds out the flaky gentlemen. The ones with volatile schedules. The ones who book with multiple girls just in case. And of course the ones that just get a kick out of messing around with other people's time.
I understand that personal information is attached to an e transfer, and that other people may have access to your transaction history - be that a partner or accountant. A work around which leaves no paper trail is simply going into a physical bank branch with cash and depositing directly into my business account.
I imagine any lady who requires deposits would have that option available to you as well.
As long as the lady has an established reputation, I think it is extremely unlikely that she would jeopardize her name for a few hundred or few thousand dollars. Furthermore, most of the courtesans I have met carry themselves with a high degree of personal integrity, which is somewhat of a requirement for truthfully utilizing that title.
If you are uncomfortable with something, then don't do it. Always listen to your gut.
It is usually the people with the most to lose who are the most trusting. This is because successful people have developed great gut instincts, and don't waste their time with people they don't feel confident in. If they don't fully trust a lady by her reputation, website, communications etc. they simply wouldn't book a meeting with her. Therefore, providing a deposit is not an issue at all.