Keep an Open Mind
If you suspect (or know for a fact) that your child is a bully, don't panic. You should be glad that you know and that you can now do something about it. Bullying is learned behavior and learned behavior can be unlearned. Your child, with your help, can learn why bullying behavior is detrimental to both himself and his victim. He can learn new, more appropriate, behaviors and he can learn to make amends for his past behavior.
The worst thing you can do, upon finding out that your child has been harassing other children, is to condemn him. Don't call him a bully and simply punish him; he will get angry and lash out in even more aggressive ways.
Instead, you want to condemn the behavior while showing your child you love him enough to help him find more appropriate ways of handling peer pressure, his feelings, and conflict with his peers. You will need to love him more — not less — in order to guide your child toward successful and healthy peer interaction.
If you get a call from a parent informing you that your child engaged in bullying behavior, stay calm. Don't automatically deny it, because it may, in fact, be true. All children have the capacity to bully. It is important to learn the facts of the situation and figure out the best way to handle it before you approach your child.