Bully at work?

[areo16]

I have an ******* at work that I'd label someone who deserves a punch in the snot box "bully". I've tried to avoid the situation, ignored him, confronted him and fought fire with fire (all verbal). But it doesn't seem to help the situation.

I work in the food service industry and I live in the US. It is a family business restaurant I work for, so I don't think management would be of any help. The person who is bullying is a co-worker.
My concerns are of course losing my job or criminal charges if I start a physical confrontation. It is in downtown of a city so the cops are everywhere. I like the job. Its great money.

I'm new to the job and I think the guy is just jealous or whatever that I've started working there. He's been there longer than I, about a year. I think it's an alpha male thing. I'm a nice guy in person, so he really has not excuse for what he is doing.

Any ideas? A shot to the snot box?