Pretty much what tiger said... I have told therapists on my first visit that I self-harm. Even when I was actively doing it, the good ones took the time to dig deeper and assess the risk I posed to myself. I have yet to be hospitalized on my first meeting with any therapist... Even when admitting suicidal thoughts, they talked to me about it beyond just me saying I had the thoughts. The times I said I was likely to act on it without reaching out for help, I was still given the option to go inpatient on my own (though I'm sure they would have sent me had I declined to choose that option).
Even in that session, you can reveal a little at a time and see how she reacts. I met with one therapist who wanted to hospitalize me on history alone... needless to say I did not reveal anything to her, but cut the session short and left. On that note, don't give up if this woman is not the right fit for you in terms of treatment. It often helps to have some questions to ask (specifically about how they handle self-harm, what their experience is with it... and other questions to get to know her style better). You are interviewing them as much as they are you...
good luck and let us know how it goes.