Obviously if you are being bullied at school or in your neighborhood, you should tell an adult immediately. It's important that the bullying stop, but there are many examples in scripture on how to deal with bullies on a spiritual level.
One of the best scriptures on how to deal with bullies on a spiritual level is found in the Gospel of Matthew. "You have heard that it was said, you shall love your neighbor and hate your enemy. But I tell you, bless those who curse you, do good to those who hate you, and pray for those who mistreat and persecute you" Matthew 5:43-44 (WEB)
In this verse, Jesus clearly tells us that we should do good for those who hate us, but also pray for those who mistreat us. It may be hard for us to accept that we need to pray for our enemies, but praying for them can be the most effective remedy in stopping the bullies from tormenting you or others. God can soften the heart of your bully and change the way they think and see the world. They can be used of God just as much as the next person. And God wants to use them. It takes considerable faith to pray for them, but God sees your faithfulness.
We should pray that we see our enemies with the same love and grace that God sees them with. This is part of being a Christian. It is not easy of course, to love our enemies, but if we pray to see with the eyes of Jesus, He will let us do just that. It is a great feeling to begin to see the world this way. Compassion is maybe your greatest weapon in dealing with someone who is mean in their spirit. Just remember that God loves them with the same love that He loves you with. He offers to them the exact same mercy that he offered you.
Dealing with a bully is not easy, but God can use the situation for His Glory and can completely turn things around for you.