Goddess, I experienced a bully at work on the last two jobs I had. The first one it was my boss. This made it extremely difficult to deal with, I kept trying to figure out what I was doing wrong. Then I realized it was not me with the problem but him. This helped me some. I had to file a grievance and as a result, they had an arbitrary mediator listen to him and me. The outcome was he was not allowed to speak to me except through a third party and a couple of other things which made it a bit more bearable.
Tolerating someone being a bully is a horrific experience. I think it was a great contributor to my depression and how severe my depression was. I still struggle with the depression and am still working through the resentment I have for this man after 4 years.
The second person was a woman and a co-worker and I simply resigned from my position. I was not going to administration about it or deal with it. I was fortunate enough to be able to make this decision.
I agree with Breanne, I hate to hear you having to go through this, but also realize that sometimes it is worse depending on who it is (boss vs. coworker, etc).
After my first experience, I googled bullying in the workplace and related terms and found alot of useful information. I think you might find that helpful.
My only advice to you is to realize it is NOT personal, it is their problem. You are not the one with the problem. If you can, go above their head and report it. It is a shame that it is not illegal to bully in the workplace. However, depending on where you live (US, Canada, etc) there may be some laws against discrimination that would assist you. You can also utilize the civil court system in the US to file a claim against someone for personal injury against a bully though it is a difficult case (so I am told).
I hope I have helped.
Welcome and if you'd like to discuss similarities, differences or your specific issues with your bullying situation, would be glad to. You've come to the right place for support with whatever issues life deals you!