I also agree with Dragonfly and avoidant. Telling her is probably your best option. She should know that anything online is fair game (unless you hacked in by guessing a password or you are some computer genius or something... then maybe it's more of a gray area.) But the thing about transference is that it really feels like you can't control what you're doing.
I told my T about looking her up online and she didn't ask me about anything further. So I didn't end up telling her (as I planned) about finding her Pinterest account and from there finding her Facebook (but I can only see the front page because of her privacy settings, so it's only two pictures.) I did tell her I felt like a stalker and that I didn't want to feel that way and that I didn't mean to do these things.
I told her that sometimes I drive to her office building and sit in my car for a few minutes.... then I sort of "wake up" and realize I'm there and think "what I am doing?" Then I leave.
She didn't seem to think any of it was a problem. I said I was afraid I was being inappropriate and she said she thought it was totally normal and everything I felt was appropriate.
Perhaps if you started by telling her you are worried about her leaving and then bringing up the online stuff? Would that make it easier?
Like the others said, don't be too hard on yourself, transference is not easy to handle and we can only ever do our best.
Hugs and good luck!