What they do is put an authorization through on your account, which is somewhat like a hold. You won't see it on your bill, but it reduces your available balance for the estimated amount of the rental. I'm about to put a reservation on my credit card. I work for the credit union that issued my card, and I can see the outstanding authorizations, but you won't see them on your bill. The rental company must have some form of security. Otherwise, they would have no recourse if they let you have the car and you didn't have the available funds.
As a side note, I'm glad that a lot of rental companies do not accept debit cards except for final payment. But even then, I would never put a reservation of any kind (hotel, air, car) on my debit card. If there's a mistake made and you have to dispute it, you could be tying up funds that you could otherwise be using for up to 90 days. You have more protection with a credit card, because you don't have to pay finance charges on any amount you dispute. Believe me, I've seen it happen.
Sheri