The thing is, you don’t know why she is showing those interest vibes.
Although you believe that she appears to be way out of your league, you have no idea what her criteria is in relation to what she deems attractive.
It’s never healthy to instantly judge yourself as not being worthy of asking a girl out on a date, based on a preconceived notion that she is way out of your league.
You seriously don’t know what she finds attractive.
When a guy hits it off with you in public and asks for your phone number, giving it out is the right thing to do.
This means that you get to continue the conversation beyond where you met him, whether it was at a gas station, coffee house, library, gym, grocery store, courtyard, etc.
Why wouldn’t you want a great conversation to continue with a guy that was bold enough to start a conversation with you that you enjoyed in public?
Granted, there is a fear that this is a complete stranger and you don’t know what he is about nor his background.