I got my assessment when I was 64...but not in Ohio. The process might be similar, though.
Check with your health insurance provider. Some of the assessment cost might be covered. Do their process and their paperwork to maximize your coverage (if any). Stay with in-network providers, if you can.
Don't assume the insurance company knows much about Adult Autism Assessments! Mine gave me useless referrals and bad information about who could do an Adult Autism Assessment. I think Adult Autism Assessments must be uncommon so the insurance company probably does not have much experience with them.
Correct information: You should get a licensed psychologist to perform an Adult Autism Assessment. (My insurance company incorrectly said the psychologist had to have ABA certification! They do not! They just have to be a licensed psychologist.)
I would be very surprised if you found a psychologist who advertises that they do Adult Autism Assessments. I suspect those assessments are rare so why advertise a service (almost) no one wants? You'll have to search.
I started with https://www.findapsychologist.org to find psychologists within a reasonable distance from my home. And I looked at their web pages. I looked for psychologists who worked with Autism and took patients my age. But I think Adult Autism Assessments must be uncommon so no one's web page mentioned them.
Then I used the telephone to contact candidate practices to ask if they could do an Adult Autism Assessment. (Maybe don't ask if they do Adult Autism Assessments because those are rare...ask if the could do one.)
Good hunting!
P.S. The actual assessment was kind of fun!
P.P.S. My experience is relevant for the U.S. state I live in. It is possible the rules are different where you live.
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When diagnosed I bought champagne!
I finally knew why people were strange.