Once my referral went through it took one week until my initial meeting - one more week (maybe 9 days tops) to the eval appointment and then three weeks until the results. All in all 5-6 weeks.
I first met with the neuropsychologist and she asked me questions about my birth, childhood, schooling and why I thought I was an aspie, if I self harmed, suicidal and about my work history and did I ever want to drive a car and how many times did it take to pass my written driver test and the driving test itself. Few other life detail questions too.
At the end of that she said she strongly suspected I was aspie and would like to do the eval my GP recommended for me.
As for the aval itself it wasn't anything to stress about. Yes, I was nervous, yes I flopped many areas, and I was horrified to learn there was a math test.. but over all... not near as bad as I had been imagining in my head. There was spelling, math, spatial, and a few things I have no name for... sorry. Shape matching and drawing and visual memory tests. Auditory story recall and a few dexterity things.
So... what I am trying to say - it isn't very scary when you find a good specialist in the area of ASD's. I have read some experiences on here that makes me grateful it was as easy as it was for me. Hope you find it just as easy.