I have also read that sometime you have to do a few other "Ask..." interactions before "Ask to Move In" comes up. This is because there is only so much space allotted to "Ask..." interactions for whatever reason and you have to get the others out of the way.
I had read that elsewhere, too, and cleared the other Ask interactions. The "Ask to move in" option still didn't appear in the menu until Agnes thought my founder Sociable.
Just had my sim autonomously be "asked to move in". I wasn't prepared for this and had to make a quick decision. The guy was still in a relationsip (though they were barely speaking), and he jumped on my sim and asked her to "move in". She moved in (he has a better house). Still waiting to see (leave them mostly autonomous) what his plan is.
Yes, it will be interesting to see what happens next.
In my first dynasty attempt (thwarted by a toasted motherboard), Agnes had asked my founder to move in, and I had to say no. Lost a sizable chunk of relationship points over that one.