I have the same desire, but I do not dare to ask for outside contact. I am crazy needy and attached, and I do not want her to think I am overstepping boundaries.
So, I write everything down and read it before the session (shorter stuff) to bring it up. Or, I write her a letter and hand it to her.

In the past, I have never dared to be this open with someone, and no therapist has ever given me this much insight and support. The wanting to be totally honest with her is a good sign for me, I guess, because I have never been honest and this open before.