pre-date sex is always the way to go. Suggest it like it's perfectly normal and standard and be a little shocked and offended if she declines.
Go to the bathroom, come out shirtless.
Phrase is like "Let's get the sex out of the way now so we don't waste both of our time if things aren't compatible."
Say it with a straight face, then undress and let her see the pecs. Boom, you're in.
Or, just keep FBing her and phone without spending a penny, then once she passes the crazy test, invite her over for a dinner you cook, Redbox and wine. Already you'll be able to interview her about food preferences, wines, movie tastes, etc. You'll spend $30 on food but have leftovers for your 11pm feeding, no matter how things go. I've never understood the need to spend $50 on a stranger in an awkward setting... save that $ until you know you like each other, and THEN it's a better dining experience to drop 50$ on sushi.