Even talking about something that may seem trivial to you can help your therapist learn more about you. The first three sessions aren't going to consist of major breakthroughs, you're not going to be talking and suddenly feel like you know everything wrong, and how to put it right. It can take some time before you feel completely comfortable talking with her about everything, which is what it sounds like to me. But that's normal, I mean, are you going to walk up to some stranger in the street and start giving them your life story?
The only downside of this is it can be costly, hopefully you have insurance or some way of making sure that you can keep talking to
someone even if it's not this particular person.
But in the end, you're going to have to be the one to really talk about SIing. She might be able to make a guess at it, but a good therapist isn't going to just start randomly assigning labels too you.
Once you feel comfortable with her, or even if you don't, but you just really want to talk to someone about it, bring it up. It might be helpful to see if she is qualified to help you with SI and everything you're going through. Some therapists only work with certain things, but even so, she should be able to refer you to someone who can help.
I guess you could start by asking her if she's ever dealt with any SIers before, what she did, etc. I wouldn't be too worried about being locked up or anything

you said it's been almost year (congrats by the way), and the fact that you want to talk about it shows that you care enough about yourself to not want to hurt yourself again.
And in the end, the worst she can do is call for a padded van, and then you'll have to escape, and move to Canada. There, you'll learn to communicates with the polar bears, and, whilst becoming an incredibly good hockey player, you'll form all the polar bears into a giant gang. Then with the help of the other tundra creatures (and all those ex hippies up there) you'll help to stop global warming and bring peace on earth and goodwill to all men (and women). Unfortunately, Hollywood will then take your story and turn it into a horrible movie adaptation that makes you out to be a pot-smoking, bear loving hippie Nazi who is trying to use dark magic, a là Voldemort, to bring Hitler back to life. The movie will have poor box office openings, and will feature a song and dance number. It will suck.
But on the plus side, they have good beer in Canada.
Good luck, and let us know how it goes on Thursday.
Also, if you think the movie-bit is insensitive, let me know, I'll take it out. Unfortunately I'm in a downswing right now, and don't know when I'm being an asshole.