Let me get a lil technical if you don't mind...
Are you nervous because a parent isn't nearby, or is it because no one you KNOW you can trust seems to be nearby? This is kinda two different things.
(I'm not saying that you actually "distrust" or "fear" mum's friend, just that she might not be proven through thick & thin yet)
If you're still "hanging onto mama's apron strings," well yeah that'd be kinda weird, most people would be growing out of that by 20, but I don't quite think that is what it really is.
Because it is VERY normal for people to be nervous/scared/panicky when alone without someone they trust-trust.
We're "herd" animals basically, and the world has a lot of big scary things in it even without worrying about lions, and bears, and tigers.
Trust worthy others increase survivability even of non-aggressive things like hunger, warmth, or assisting with accidents big or small.
Psychological comfort is no joke also. And predictability. Even the psychological aspect of being needed is quite important.
I think you're very normal that way.
People on the spectrum can often see or comprehend more possibilities for things going wrong and usually have more experience with things going goofy.
I'm saying I think it's normal to have the level of anxiousness at being 'alone,' but having Asperger's may make it harder for you to distract yourself and/or to believe "everything is going to be fine."
I don't think you're weird.
I suggest finding some things highly interesting/engaging to do (especially, to do with the stay over friend) as a distraction.
Or beer. =)
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(14.01.b) cogito ergo sum confusus