How do you ask a woman out on a date?

There are three possible things going on here. Here they are in order of likeliness (sorry)

1. They are a friendly person who likes your coat.
2. They are flirting, but in a friendly way and don't want it to be anything more than that (yes, this is a thing!)
3. They are flirting, and want to get to know you more.

But your question is "how do you ask a woman out on a date?"

So here's my answer...

Say, "I know that this is a long shot, and I feel a bit awkward about this, and I promise that I will never bother you again, but... would you like to go on a date?"

Be prepared for the worst, and hope for the best.

If they do not say yes, then apologise for making things awkward and wish them a good day and leave. DO NOT TRY TO CONVINCE THEM OTHERWISE!!!! Then go off an lick your wounds like millions of us have done (autistic or not) since time immemorial.

If they say anything other than yes, they have said no (this is hard for autistics to spot.)

That's really good advice, thank you. The emphasis on awkwardness seems a good way to approach things as indeed it could be awkward since it's somewhere I shop a few times a week so I would probably see her again.

That's really good advice, thank you. The emphasis on awkwardness seems a good way to approach things as indeed it could be awkward since it's somewhere I shop a few times a week so I would probably see her again.

If in the UK, maybe swap in Moonchild's 'like to go for a coffee' instead of my 'like to go on a date' ('date' is very American, I think,)