Seems to me it would be incredibly awkward to just ask her out, out of the blue. She knows nothing whatsoever about you.
I would go up to her and say, “Hey, it occurred to me, Isn’t it silly that we pass each other by without introducing ourselves? My name is x”.
“Hello x, my name is y”.
“Pleasure to meet you. Have you lived here for a long time?”
Let a little more small-talk flow and then end the conversation.
“I’ve got to run but it was nice meeting you. I’ll see you around.”
You’ve demonstrated some initiative, boldness, and a casual, light and fun vibe.
The energy flowed from you to her. Very important.
At that point she will do what she will after that interaction. If she is intrigued, she will make it known to you in future interactions. If not, she will be standoffish.
Either way, you have handled your business and you will feel good about yourself.