Like Katie, I told my therapist I already knew my gender, and didn't need another party to confirm it. She gave me my HRT letter.
I asked about SRS, and RLE. She said my RLE was done, as I had been full time for nearly two years, and to call her for my SRS letter. No further meeting with her nessasary. She said I would need another letter from a psychiatrist, but that was a one time evaluation.
So, in short, one meeting with each.
Things that got me fast tracked- I was fifty four, and fulltime. I live in Canada, where, in general, your legal gender is taken as what you say it is

I was presenting with some serious GD, so my Drs. wanted to get me going PRONTO. I went in very well researched.
I would think a younger patient may meet more gatekeeping, as they really want to dot their I's and cross their T's before consenting. Good luck!