So here's how it typically works, at least as far as it has been for me: if you do the inviting, you pay for both. If she does the inviting, you either go dutch or she pays for both of you. Since she's the one doing the invite (and therefore should know the pricing at the place you two are going), she should be prepared to pay for herself at the very least. Note: just because you're not paying for her doesn't mean she won't like you, nor will it mean she won't get physical with you in some way. Heck, some of the best dates I've had ended with me and a girl hooking up, and I didn't spend a dime on her!
One thing I would do if I were you, though, is to limit the texting. The more you text a girl in the beginning, the more likely she is to see you as just a friend since, by texting her constantly, you're essentially in her presence all the time. This also makes it more difficult to tell if she's inviting you out as a friend or as a guy she could potentially see herself with. If you had been texting her less, this invite would be a definite sign that she's into you. Regardless, I treat all outings with women as dates, even if they're just friends of mine. Where that date goes, however, is up to you, so make it count!