It sounds to me like the pre-authorizations from your re-bidding are taking a long while to be removed from your debit card. This is often a problem at hotels, too, which will pre-authorize an amount when you check-in, for incidental charges. The hold-funds is placed immediately, but can take up to a week for the banks to lift after being released by the hotel (or Priceline). For example, if you have $600 in the account and check in to three hotels over three days, and each hotel preauthorizes $200, after the third check-in, you will have zero available cash in the debit account, until those pre-authorizations fall off. In the meanwhile, you will not be able to withdraw those monies from your account, and checks may bounce if it is a checking account. This is why it is NOT advisable to use a debit card, if you can use a credit card. Credit card preauthorizations are removed immediately.
Regarding your main question, I think you have nothing to worry about, for two reasons. Firstly, Priceline will not try to charge your card again unless you return to that TryAgain-screen and click on "Buy My Hotel Room". Secondly, if you do try to double-book, Priceline automatically looks for overlapping bids and trips to prevent inadvertent duplicate bookings, and will give you a warning screen about it, and present you with an option to proceed or cancel. I found that out one time when I was buying a room for my Dad in one city, while I had a room already booked for myself in another city for the same night. Finally, if for some reason you do end up with a double booking, Priceline would likely have no problem canceling the duplicate for you, if you call them.