Dinner, BUT that will definitely put her on the spot and I can either quit wasting my time and move on to someone else, or she will say yes and we can go to dinner.
TERRIBLE idea to put her on the spot. Even if she says yes, it likely won't end well for you.
1) putting her on the spot really just means she's feeling preasured, and with others listening, she'll feel preasured to say yes. So that'll mildly piss her off.... or maybe not so mildly, I don't know the girl.
2) if she says yes, it might not be because she actually wants to. Like I said, she'll have others watching/listening. She might be afraid of seeming mean if she proverbially shoots you down like a Ju-52 with a fighter on it's tail.
3) if she says yes, and didn't want to, she'll end up resenting you for both putting her on the spot like that, AND making her go on a date with you.
Nearly all possible outcomes are negative.