If a bus driver said to her, as per the OP, “That’ll be two pound ten please babe” then I would think absolutely nothing of it. And she’d be quite happy to be called babe.
Likewise. And I think I’ve just spotted what might be causing the disparity. Compare,
“That’ll be two pound ten please babe”
“That’ll be two pound ten please, babe”
The first, a throwaway friendly term. The second, the emphasis moves, he’s making a point of calling her a babe.