Seeing an ex-date in public

I (M29) went on a few dates with a woman (F27). We both had a great time, but ultimately decided we weren't in the right place to pursue something long term. It ended on good terms.

Fast forward about 5 months or so. I'm putting myself out there again and have just moved into a new flat across town. A couple days ago I'm driving about 30 seconds from my flat and I see her walking in my direction.

I felt like I closed that chapter and had moved on, but seeing her again, seemingly living close by, has got her in my thoughts. Not to mention I'll be walking that way frequently, only one supermarket near by, etc. Wouldn't be surprised if we bump into each other.

Anyone have any experience/advice with a situation like this? I liked her a lot, so wouldnt be opposed to catching up or seeing if there's anything more serious again. It's just thrown me for a bit of a loop.

Extra: I posted this in r/Dating over a week ago and just saw her again yesterday. I was of course driving again so couldn't say hi.