That IS strange. If it were me, I'd smile and say "hello" or give her a friendly nod the next time you see her. If she recognizes you or acts surprised, you can say "We appear to be frequenting the same establishments - feels like we've become friends (or neighbors).

Who knows, maybe she is someone you're supposed to meet. Maybe she has an interesting character. Maybe she'll just think it's weird too. Or maybe, she'll just give you a dirty look and tell you to mind your own business.