Do you think there a reason why you feel the urge to see her out of the sessions and put yourself in the situation of bumping into her?
Is it curiosity? hope to have a conversation out of therapy? Want to connect more often than your sessions.
I don't think you are wrong or anything for this a T can have so much positive power over your life and we develop strong bonds.
if you are aware that you live and work close to each other then there will be times you cross paths. I think that it would be good to work out what boundaries you will place on yourself when your paths cross.

I dont know where my T lives but she works near my house thats why I chose her. I have seen her in public 2 times in 6 years. Once in the supermarket and once in a restuarant with her family. In the supermarket I stopped to say hi and when I saw her with her family I just pretended that she wasnt there.

Your T might think that you are seeing her by coincidence but she also may think that you are following her.

I am sorry that you are going through a divorce that must be really difficult. It can be really tricky especially if you have kids i dont know if you do or not but i have seen how hard it is for my best friend to go through divorce with kids. Maybe your feeling that you need to make an extra connection to T because the instability of your marriage ending.
either way hugs.