More on being Bullied from a posting in the US News..

3. Document your situation. Get in the habit of noting what happens with this person and when. Keep a detailed log regarding your interactions—what he says and does, as well as what you say and do. Documentation will be your biggest ally should things take a turn for the worse in the future. And, of course, remember to always act in a way that you can be proud of. Don't let the bully push your buttons and bait you into an emotional reaction.

4. Get superiors involved. Unfortunately, there may only be so much you can do on your own in this situation. Bullies can be stubborn and irrational. Often, when it's gotten to this point, there's no use trying to simply sit down and hash it out with the person. You need to call in the cavalry.
Again, be sure you have your documentation in order and that you've objectively looked at the situation. Then, take the issue to your Human Resources department for help. Describe what is happening in detail and explain how the situation is impacting your ability to do your work. It's important to stress that you want to find a productive, comfortable way of addressing the situation.
In most environments, HR is your best bet for action. If you choose to go to a trusted supervisor instead, he or she may not want to get involved. HR, however, is specifically designed to handle these kinds of complaints. That doesn't mean it will always be addressed as quickly or effectively as you'd like, but they typically have more experience and a greater interest in resolving the issue, as they understand the potential legal ramification if the situation escalates.

5. Move on. Bullying left unchecked can harm your mental, physical, and emotional health. If you've done your best to manage the situation and you've sought assistance from HR but still no improvements have occurred, it's time to consider moving on. No, you're not letting the bully "win." You're simply taking care of yourself. You won't prove a point or teach anyone a lesson by staying in a dangerous situation. Everyone deserves a safe, comfortable work environment. If your current employer is not able to provide that to you, take your skills elsewhere.