We went through this exact sort of thing last week, actually.
We'd been seeing our current therapist for about a month and couldn't figure out how to explain things about our life to her without explaining "us". So we made an agreement to tell her, even though we were extremely scared to do so because we didn't want to seem crazy or risk telling her and having her not believe us. Flat out telling her was out of the question as that would have been so stressful we couldn't have done it.
We ended up writing things about us and our dissociation on three sheets of paper. The first one just mentioned how severe 'my' dissociation and time loss was, the second described things in greater detail and explained that 'I' became different people at different times, and the third one explained a specific event in great detail that included the names of the four who had switched during it. We started off our session by telling our therapist "There's something I've written that I'd like to show you." We figured we could show her whichever pages we were comfortable with. For example, if we chickened out we could just hand over page one which only included a bit more information on things we'd already talked about.
In the end, we gave our therapist all three pages. She had a lot of questions for us and it took a long while to explain to her that it wasn't just that 'I' acted differently in different situations, but that it was actually multiple personalities sharing the same body. She finally had an ah-ha moment and said: "So, you're like a spaceship! You all exist in the same thing but there's lots of different crewmembers who take turns being captain!" Close enough.

Even though it went pretty well, telling our therapist was really hard. We were panicking as she read the papers, wondering what she would think and what she would say. We psyched ourselves up that it would inevitably end in disaster and honestly struggled to not run out of the room while we were waiting. We had thought about sending her an email instead or just giving her the papers at the end of the session, but the anticipation would have been too much. Giving them to her face-to-face allowed us to face our fears and actually talk about things we never thought we'd be telling anyone ever. Even though it was difficult, we're confident it was for the best. After all, how much can someone truly help you if they don't understand what your issues really are? Or the extent of them? If you've been seeing your therapist for three years, we'd guess that she probably has at least some idea of what you're going to tell her.
However you decide to go about telling your therapist, we wish you the best of luck!