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I can see where you're coming from with not wanting to befriend her. But we used to talk a lot when we were going out. So when she sees me online, she'll occasionally talk to me about whatever. What do you think would be a polite way of asking her to stop without making it seem as if I'm just avoiding any friendly talks?
Well, tell her you got something to do and go do it, or simply take your time to answer and make it short and simple.
Also, don't keep pushing. You have already invited her, possibly more than once. Whenever she'll want to go out with you she'll ask for it, so don't ask again.
Don't freeze out, don't go "all in", just... forget.