this is something that I've always wondered. Why did everyone call her Aunt Bee when she was Andys aunt, and noone elses?

I guess for the same reason everyone on THE BEVERLY HILLBILLIES called
Irene Ryan's character "Granny" -- when she was only Elly May's grandmother
(on her mother's side).

I think that was good that everyone called Aunt Bee on The Andy Griffith Show

Yes, it seemed to fit like a term of affection.