I think a lot depends on where you are and who you see.
I went to a GP (who I hadn't seen before - much easier for me to talk about it to someone I didn't know). I booked the appointment online and where it asks what appointment is for I said I thought I might have AS, so I didn't have to say it to anyone. She made me say it anyway when I got there even though she'd read it, and that was probably the hardest bit of the whole thing. I had written a massive list of everything that pointed to it and she then read that and said it seemed reasonable and she'd see if she could get funding to send me to Sheffield for assessment. She also asked if she could copy my list to send to Sheffield (and probably to the funding people). Funding approved after a few weeks/months and the Sheffield appointment was about 9 months after initial GP appointment. They told me on the day they were happy to give a diagnosis. Sent paperwork through, had follow-up appointment a while after.
But what made it possible for me was the written list. I'd done loads of research online and through books, having suspected for a couple of years but people had laughed it off as a joke if I ever mentioned it, so I was a bit secretive about it and didn't like to talk about it. Everyone seemed to think I was fine so even now I sometimes feel a bit like a bogus person. But from my research I'd written everything in my life that made me think I had AS, past and present, and related it to the research where appropriate. Eg. some people finding me rude even though it is my life's aim to be polite and please people, having problems at school with wordy maths questions even though good at maths, stims that we never realised were stims til then, sensory issues, interests that others think are obsessive, not liking eye contact, hating unstructured social situations, not knowing what's expected. etc etc. Things inside of me no-one else knew about, things people had mentioned about me that I had never noticed, things that were obvious to the world, it was all in there!
So I would suggest write it all down. If, like me, you struggle to get your point across when talking (I chicken out/get mixed up/forget things/think I've said too much or people must be bored of my voice) it will show whomever you talk to the true extent and variety of all the issues you are having.