There are many reasons why a bully is a bully. In order to properly "deal" with a bully you need to know more about him/her. There isn't just one single solution to this problem.
What people tend to overlook is that while the bully is hurting someone else, they are hurting inside themselves. Their behavior is due to a need of theirs not being met and bullying others is a way to meet that need.
It could be a matter of wanting power, control, or love. It could be a desire to be noticed, recognized, or respected. There is just so much that goes into why people do what they do.
The best course of action to take is to try look at what the bully is saying or doing, possibly speak with the bully or his/her parents (depending on age) to try to find the reason behind why it is happening. Unless you get to the heart of the issue, it isn't going to stop. You might get the bully to leave one person alone, but they will find someone new to attack and that isn't any better of a situation.