You can't see a way to transition it because there isn't one! Like you say, the bar is busy, she's at work. She's got things she needs to do. How, if the bar is packed, is she going to justify standing still talking to someone?

If you like her, tell her 'I can see you're extremely busy right now. But look, in a whirlwind of forethought, I have scrawled my telephone number on this small piece of paper. Telephone me at a time which is more convenient, and we can go and drink tea together.'

Yep?