It honestly took me over a year to get comfortable enough with my T to be able to talk to her like a normal person. There were sessions when we would just sit in complete silence because I couldn't say anything.
What helped me was being able to email her in between sessions (although email can be a very tricky form of communication in therapy so beware), so for me, it was a way to get the really hard stuff out and feel like I was connected to her in between sessions.
I think that writing a letter is a good idea; I can honestly say that if it wasn't for me being able to to write to my T then I would not be where I am in today in therapy and my relationship with her would not be as close.