HTC, sounds like an awesome date. I might even enjoy dining out with you if we weren't both so damn ugly!
I've never caught a girl peeking at the bill, although I don't try to catch them peeking, either. I pay reasonably discreetly because, well, I was just taught that whomever pays the bill does not draw attention in any way to the cost. I know no girl has ever picked up the bill or opened the folio in front of me, but it's possible they can read the bottom line when I'm holding it in my hand or writing the tip. (My 50+yo eyes couldn't see that from 2-3 feet away, but maybe hers can!)
If I left my bill or folio or card on the table and left her there while I used the men's room, I have no doubt that some peeking would be going on. But I don't do that.
But they all see the menus and the prices. Even the ones who like it when I order for them and look forward to it ("I just trust you, Daddy.")

So they have a rough idea of the outlay. At least I hope they do.
Two weeks ago at an upscale steakhouse in a major eastern city, my petite Asian stewardess told me the only time she eats steak is when she's with me.
There must be girls out there who sort of "resent" the costly restaurant bill if they think the money "should" be going to their pretty little selves instead. But none of them have telegraphed that to me.
I take a girl out to a fancy place because that's the kind of evening I enjoy, not because I think an expensive meal will help me get her panties off.
Rockford