Not A Bully
Bugs’ creators wanted to make sure that he didn’t seem like a bully. That translated to the fact that Bugs never actually started any fights and always continued the fights in order to defend himself. You might notice that other characters like Daffy Duck and Elmer Fudd are the ones who start to pick fights with him.
A Brooklyn Boy
While he’s always seemingly on his way to Albuquerque, he was actually born in Brooklyn, which is why he has the signature accent. Even though his creators said that he is from Brooklyn, of course the animators came up with the character in Los Angeles, where the studio was.