That happened to me twice when I was young free and single, once while I was working in a shop and she was a customer. I got to deliver to her mother's house and got a date off her while delivering. Went out a few times. Finally broke up.
Another time was on the escalators on the London Tube, she was on one escalator, I was on another both going in the same direction. Approached her at the end, got her number and phoned her. Unfortunately she was an American living in Scotland and was going back to the States in a couple of weeks. This was before mobile phones were invented we spoke on landline a few times but then I phoned and it was disconnected.
In both the above cases we almost stared at each other, looking eye to eye, when we initially met I mean.
My guess is that if this is what happened to you, she will really want you to ask her out. That is just past experience. I am no skilled pua.