Well, I actually got super lucky regarding hormones. At least when I finally got them, I've spent a year trying.
I went in for an appointment with a therapist for the first time and got my letter right away. I had been seeing someone in my university city for two months prior but had to move for the summer. A friend of mine recommended this therapist. I had been on T illegally before, so got my letter right away. That same day she was able to get me an appointment with a doctor and get a prescription written. And I got it filled and took my first shot that evening. So for me, I had everything done in one day. This was in Alabama, though I'm back in Tennessee now. I took my 5th shot last Thursday, but I'm taking them weekly rather than biweekly.
But I've heard longer from other people. I don't know if my situation is common, but I think that the time may very greatly.