Does she try to get physically close to you? It seems odd to me that she would do that without asking first if it's okay with you? Or does she?

Yes, I have had this experience, but was too embarrassed to say anything about it. My T picked up on this and very graciously offered to keep the door open during session. He maintains a solidly respectable four feet of personal space, and both of these things helped enormously. That and time. How long have you been seeing this T?