I'm also on the autism spectrum
(social anxiety also, but has gotten much better during the last years; no trace of ADHD though but of the of the opposite type "hyperfocus, always very much on time, has packed everything, takes care of all the paperwork in the family so everything is done correctly") with AuDHD husband.
I'm not taking my dragon outside (especially I would not do so to places I have problems with, so places that are crowded, loud... which my dragon for sure also would not like). I have a harness and leash for my dragon so I can take him safely on the balcony (we're here on the 13th floor and he might get spooked by the vultures of which we have many here and I just fear he might jump/ run down without a harness) and hopefully hiking soon.
Also, my dragon doesn't want to be out of his enclosure that often (this week e.g. it was on two evenings for approx. 20 minutes each), so what I do is in case he wants out and it's still during daytime I go with him on the balcony (it's always warm where we live). But it would rarely be able to say "I want/have to go somewhere now, let's get Taco out and take him with me". I would have to force him out in most cases. And I wouldn't do so, except for an emergency. (If he would be sick, I would go and get him, but just for me, to have him around... no. If he wants to stay more in his enclosure, if he doesn't want to come out much, I respect this as his personality, just like I want people to respect that I'm not that much fond of doing things "most people like".)
I have the harness from "Nectarlee", and I use it without the wings (they can be detached easily). I like it because it holds secure, can be put on easily and is not catching on his scales and spikes.
I'm not using a sling/ bag or blanket for my dragon; he has so many spikes that easily catch on all kinds of fabric (he's a standard dragon, not a leatherback or such, has tons of spikes and very rough scales, and honestly, I love touching those, the different textures of his body).