you're not actually in charge of her or hold some other position of seniority that she's trying to suck up to...
and
There's no other legal or ethical or moral reason you shouldn't be getting involved like that and no workplace policies that would get you or both of you fired...
I would try (as casually as possible):
"Hey I won't take it personal if the answer is no but you seem really cool, are you interested in getting to know each other outside of work?"
If the answer is no,"Alright! I won't bring it up again!" And either move on to the next subject or go wherever you were going to go next and just act like it never happened from then on out.
If the answer is yes pick the closest cafe that's not a chain and is rated at least 3 stars and ask when she's free. Asker pays for askee but don't fight her if she wants to pay.