walkingblind I am very sorry this is causing you so much distress.
I agree with the comments from SpotOfWeather.
I think basically, in your shoes, I would say enough to put her off without upsetting her, and I would not mention autism unless you want to tell her.
I'd also decide whether a text or a personal word with her is better for you.
I think I'd say something like
"Thanks for the invitation over to your house. There's a lot going on for me at home at the moment so I hope you'll understand I'm not free."
If she is a normal person she will most likely do one of two things, say fine and understand or, if she is a pushy person (like me) she will say 'Oh well maybe next week then?"
Be prepared if she says this to say something like this just explain...
"It's very kind but it's not possible for me at the moment. I do hope you will understand."
And I would be tempted to say something like "It's not personal, it's circumstances for me.!
I'd say all that with a smile.
She may think someone is ill, she may think you are having your house renovated, she may think you have a very demanding job!
But you have not lied, you have not revealed your personal and private information and you've made it clear she is barking up the wrong tree in wanting to be friends with you. It sounds like she is over the top with others which is a shame. But it is not your problem, you did not create it and you are not responsible for it.
I think being vague is best. If you have not chosen to tell others about your autism through your own choice it does seem wrong you should be forced into telling someone through circumstances.
Good luck.