The short answer is to grow a thicker skin and stop caring about them -- usually there is a reason the bully is bullying, and it's a problem they have, not you. You need to remember that it's not your problem, because they're trying to make it your problem in order to feel better about themselves. Maybe daddy beats them at home or whatever and they want to take it out on you to feel better. That means letting them get in your skull is giving them what they want. So you're winning when you don't even let them factor into your life. Don't try to please them, piss them off, or whatever -- tune them out, basically. 

(If they do you physical harm, of course, you gotta do something...but I suppose as an adult, that doesn't come up much anymore. I think minors should be able to fight a bully in scenarios of physical self-defense without punishment so long as they don't provoke, but that's me, thinking that people who fuck with the bull should get the horn.)

Don't give them what they want. Develop a thicker skin and a critical eye and figure out what's eating them. The only people that bother to bully are people with something to gain, so they're trying to impress someone or feel better about themselves. It's not as much about you, the target, and your problems as much as what they're trying to overcompensate for and that they think you're the weak meat. When you go in knowing that, it's easier to mentally tune them out and present an unsatisfying target. I work in a pretty harsh professional environment with some scumbags (kitchens haze and are often abusive, especially for new hires), and my process for dealing with them is that when they cross a line, I make a note to stop caring what they say or do. I cut them off. I'm still polite, but I also know that they aren't worth my time.