I just did this for the first time with my T in my last session. There was something I was so embarrassed to tell her so I wrote it down and gave it to her like 10 minutes in. It was horrible sitting there and waiting for her to stop reading it, even though it didn't take that long. But I am glad I did it, b/c I would not have been able to talk about it.
I would suggest giving it to her at the beginning of session, that way you can talk about it the rest of session. I know it may sound easier giving it to her at the end, so that way you can just run away and don't have to be present while she reads it, but I think that ultimately giving it to her at the beginning is better so you have time to talk about it b/c what might happen is you might give it to her at the end of session and leave and then next session not talk about it because something else has come up or whatever.
So yeah, I just wrote out the situation that I didn't want to talk about out loud and told her I wrote something that had happened and then I gave it to her. I know that I would not have been able to say it out loud, I would have frozen up, so it worked for me. Although it was painful waiting for her to stop reading it.