I think no matter what, on the date, pay or not paying, if she doesn't like you, she doesn't like you. That's really the bottom line. I feel above all common courtesy does trump all. So, to pay for a date YOU invited her to is not to handicap your chances she'll sleep with you, but rather a backhanded attempt to get her to sleep with you. If these are not your attentions, you may as well skip the meal altogether, and as another poster mentioned go to a free activity. I see Chase's logic though, but rudeness is never an excuse to be a human being up front.
As a solution, us menfolk could use this opportunity to break the tension with a little levity in regards to this dilema. "I'm picking up the tab this time, Missy, but next time...you choose where we go and you're paying. And I'm not a cheap date." Then flash that winning smile. I think it opens up the possibility of future boink-fests.