If i give her mine then it tells me if she's really interested if she contacts me. But if she gives me here then I can contact her and she can either ignore me just the same or I can get myself in her memory even if she forgot or wasn't gonna call me at first. Which is better?

For me it's practically easier to just hand her my number after we have been looking at each other for a while on public transport. I'm so beta that I feel a lot more capable of doing that right now than asking for her number. But maybe that's asking for a rejection?