bella thought those vampires won't approve of her, correct?

I didn't perceive Bella as being frightened. Curious yes, nervous....... definitely, but frightened? No, not at all.

Edward describes his family as being incredulous; Bella states they don't like her. he doesn't have much support in his relationship with Bella (only Alice backs him up), but he says their biggest question mark comes from the fact they don't understand how or why he feels the way he does, and why he can't leave her alone. They feel threatened not by her presence, but rather than by Edward's emotions.