I'll tell you exactly what I would do and say, but there's a problem with that. If you do it, you'll be impersonating me - and it's not me she gave the number to - it's you. She might just want you to be yourself. Anyway...

I'd call her tomorrow, making my best guess when she isn't busy and say, "Hey, I have a question for you. When a really cute girl that you're desperate to get to know better gives you her phone number, how long should a guy wait before calling her - you know, so he doesn't sound over eager or something?"