I would first find out how she sets up new patients. See if she does an initial assessment/intake appointment or if she is more casual. I think if you are going to email instead of call I would set it up by saying you are looking into individual therapy sessions and would like to know about setting up an appointment to see her. If you feel comfortable you could say therapy session for an eating disorder, but I wouldnt put many details into an email. I think that is best left for more personal forms of conversation (phone, in person, etc). Also, you mention concerns of payment. I would ask her about her rates and what insurance she takes (if you have insurance) and if she offers a sliding scale or would allow payments in installments rather than all at once.

Good luck.