It depends on your doctor if you have to go somewhere else for the blood to be drawn. I had to go to a lab across the street where you walk in, hand them a sheet of paper, they take the blood, and then they test it for whatever your doctor wants them to. Then, they send the results to the doctor so they can communicate them to you. You get sent the bill in the mail.
The number of visits it takes to actually get the T script depends on your doctor. They will likely wait to get the blood test results back , so probably at least two visits - though I have heard people get the script on first visit. Your second appointment will hinge on how long it takes to get the bloodwork back and how long it takes to get an appointment at that office generally. Even if they take the blood at the office directly, it is still usually sent to a lab for analysis, no matter who the doctor is - specialist or primary care.
in addition to blood work, I have heard of people having to get a pap smear before they get a T script, but they did not ask me about it when I started.
if you go to a specialist like an endocrinologist instead of a family doctor, it will be the same as visiting the family doctor in essence in terms of getting on T. They will ask the same questions, do the same tests - the only difference is they have specialized knowledge and experience that can help know more about how to approach problems. However, It does not really matter which type you see - instead you want to work with someone who has experience treating trans patients, bottom line, no matter if they are a family doctor or a specialist. If you got referrals from your therapist, you should be good to go on that front.
