Start doing crossword puzzles.

Find the weirdest question on there "American Ostrich" for example, and just ask your target, confidently. "Hey, what's another word for an American Ostrich?".

She'll be completely surprised, at which point, show that you're doing a crossword. If you pick a hard one that she won't get, you can start teasing her.

"Pffft, you don't know what an American Ostrich is?". If she gives you an answer that's too many letters, write it in, and then go "pffft, you've messed up my whole crossword". If she asks you how many letters, tell her that it's easy, and she shouldn't have to ask. Take it on from there. DO NOT, keep asking her questions. 2 as a maximum, if you're feeling persistant. Make sure to only keep the focus on the crossword for a small amount of time, switching out, preferably after her first guess, or it gets tedious relatively quickly.

After you've asked her the question, you can gauge her interest. If she seems annoyed or weirded out, you can immediately just say 'thanks' and get back to what you're doing, without embarrassing yourself in front of a crowd of strangers. If she's smiling, just take it from there; there's a lot of ways you can keep going.

Bear in mind that a lot of confidence is needed for this; it's pretty easy to end up looking nerdy.