It all depends on the therapist. Some will write the letter for you even before the 3 month mark and have you find a doctor while the 3 months expire, some wont. Mine, I had to see once every week for a couple weeks, then once every other week for about 2 months and he wrote a letter and said "theres no reason for you to come back here until you're on hormones" ... honestly I never went back, just got on hormones! But you have to do what works for you, your doctor, and your endo. Some doctors will not prescribe you anything unless you're actively seeing a therapist. Also, don't think that just because you go in as girl mode that he is gonna write your letter any quicker. They have to find out if you're abusing substances, make sure you do not have any mental problems, and be certain that you are transsexual, and not another form of transgendered, before writing that letter!
Honestly I probably lucked out in that my therapist was one with little experience and my doctor was eager to have me as a patient because she's never had one that was just starting HRT.