Oh, I totally love this topic.
In your case, be extraordinary, chuck your bad conscience and don't offer to pay for her next time around. She can only think the better of you for it, no matter what.
Where does your bad feeling come from anyway? You said you wouldn't think twice about it if she was a guy, and I guess, even if it was a poor guy, you wouldn't think about it, cause you'd expect your male buddy to have his pride.
And then this logical question: If you feel bad about being invited by her, what exactly makes you think it'll make her happy to be invited by you?
I've been on the other end of this "guy offers to pay" situation myself, so I'd really love to know and I think you'd benefit from uprooting the reasons beneath feeling and thinking the way you do as well.