I would be shocked if a T would accept clients as friends on a social networking site, for the confidentiality reasons mentioned above if nothing else. And I think your point about not necessarily wanting her to see everything you do on FB is good too -- you are entitled to your own boundaries/privacy too and that's a good thing. I would think very carefully about whether you really want that boundary removed, from your perspective...

Maybe you could talk to her about this in your next session? Just explain how it's wierd for you, because the therapy relationship is so atypical of other relationships, and it makes questions like that come up. There's no reason you can't talk about the weirdness of it, without you actually putting yourself out there for rejection.