Show some compassion
Oftentimes bullies behave the way they do because of a rough home life with poor role models. They may be bullied and abused themselves at home, and the only way they can find any control in their lives is to act out at school by bullying others. In no way should you condone a bully's behavior. However, you should show some compassion to her situation. As the saying goes, "Hurt people hurt people."
Try to find some common ground
Though at first it may seem like you have nothing in common with your bully, try to learn more about the person to find some common ground and interests. By presenting yourself in a confident manner and showing that you and the bully are not that different, he may begin to realize his behavior is not appropriate and that you two are more similar than he first imagined.
Invite the bully to activities and events
Provide the bully with an opportunity to participate in positive activities with you and your friends. This will help him learn better social skills and encourage him to become a friend. It's important to involve your other friends and hang out in a safe place with adults around, so that you are not in danger in any way.
Reach out to the bully's friends
If you can't make any headway with the bully at all, try to reach out to her friends. If her friends interact with you, then the bully may be more apt to accept you as a friend and stop seeing you as a target.
Never use violence
Even if the bully doesn't accept your olive branch, you need to take the high road. Don't stoop to his level and begin using anger or violence yourself. This will make matters worse, especially if the bully feels humiliated or threatened by your actions. Unfortunately, some bullies are going to be resistant to your attempts to befriend them, no matter what you do. However, you should at least try to reach out and make friends out of your enemies.
Keep in mind
You don't have to deal with bullying alone, so don't keep it a secret. Involve your parents, a teacher or another authority to help you deescalate the situation.
More about bullying
How a bully can change your life
Is your child being bullied at school?
Protecting kids from cyberbullying