

If you walk up to random people in a cafe, park, or embankment (really?) and ask for their numbers
So I think this is the disconnect. This isn’t window shopping; you’re trying to connect with another human being. You need to take the time to talk with her, see if she shows interest by engaging and encouraging the conversation, and if there’s any commonality or chemistry between you.
Then, if you think there could be something there, offer to give your number rather than ask for hers. It will help her feel safer with you, and she can choose whether or not to accept and if she takes it, she can choose whether or not to follow up. It puts the onus on her to move things forward.
OP’s parents are in their sixties; they probably were born in the mid '50s to mid '60s and started dating in the '70s/'80s. Courtship probably didn’t factor in unless they’re Mormons or something.