It's important to stay in control when dealing with bullies.
The American Management Association (AMA) advises:
Don't return an offensive comment. Usually, a personal attack expresses another person's issues, not your own. When you become defensive, it tends to make the other person's accusation look more truthful. (As Hamlet's mother says, "The lady doth protest too much, methinks.")
Excessively defending yourself makes you look insecure, lowers your status, and gives the other person more power to manipulate the argument's terms.
Save your anger for something else. When you react and lose your cool, you get involved in the negativity that the other person is creating. Channel your anger into something more constructive and have the final laugh.