Welcome to the forum.
You're not dreaming about what we say. We quite frequently say "I'm going to the dentists" (or just "I'm going to the dentist"). However, when we write it, we do tend to use the apostrophe, but not the final "s" (after the apostrophe). You will see it with and without the apostrophe though.
I'm going to the butchers after lunch.
I'm going to the butchers' after lunch.
I don't know anyone who says "dentist's studio". In BrE, it's a "dental surgery" or the "dentist's surgery".