I think the note writing is one good idea. Also, keep in mind therapy is not usually a short term thing. When you bring up easy things to talk about you will become more comfortable with her. Then you may find it easier to talk to her about more personal things. Nothing you tell her will surprise her or be something she hasn't heard before. What do you mean "we" have only had on session with her? Do you go with someone else?
Please pm me if you want to talk.
good luck. glad you're getting therapy.