To me, it sounds like she just wants you to share when you feel comfortable that opening it up won't cause it to leak out into the rest of your life. "Contained in the counseling process" means that the emotions that get stirred up should stay between the two of you, during your counseling sessions, and that they won't come up and surprise-attack when you are not in a counseling session. Does that make sense? I'm no expert... That's just how it seems to read, to me.

I very much doubt that she wants you to be able to talk to her about it without acting like it bothers you. That would be pretty much impossible, and contrary to the whole process of healing in the first place. Sounds more like she wants you to be comfortable and to feel safe enough to share.