How to handle bullies at work:
First rule, take action against the bully. Ignore the problem and you will either wilt under the pressure or walk away in circumstances that might be hard to explain to another employer. Try these:

Deal direct with the bully

• Explain how you feel. Say that you find this sort of behaviour aggressive and unacceptable. You believe that it
  could be classed as harassment. And now that you have explained how you feel, that you would like this not to
  happen again. If it does you will need to take further action. 
• Stay calm and civilised. Give examples of the problem (try using the words ‘I find X aggressive’ rather than ‘You
  are always putting me down’). Be specific and be neutral. Then ask them to stop. That may do the trick, especially
  with people who don’t realise that their behaviour is interpreted as aggressive. 
• Act quickly, but be composed. It’s critical to be calm when you make your move, so if you need to take time to
  compose yourself, do so. But try to act as soon after an incident takes place. If you can’t face your work bully,
  it is fine to write instead. 
• Keep a diary of incidents. Note down times, places, witnesses, and what happened. This gives your complaint
  evidential backup. Even if a change of behaviour is promised, keep hold of this record, just in case. 
• Ask your colleagues if they find the person difficult to deal with. You may be surprised to find that you are not
  alone. At the least, you now have someone to talk to about the situation, and at best you may have a stronger
  case if you take things further through the grievance procedure.

Get outside help

• If you are a member of a union, speak confidentially to a union safety representative. He or she will not take your
  complaint further than you want. But they could speak to the person, help you make a complaint or just give you
  advice. 
• If you have evidence such as a diary, try speaking to the bully's manager. 
• Go through the official bullying reporting process. Every company should have one, enabling you to report the
  problem in confidence. Check with personnel, a trusted manager or an occupational health officer as to what it is. 
• Talk to your doctor. He or she may give you time away from work to regroup. Or professional counselling,
  coaching or assertiveness training could help.

*Sources: Andy Ellis (Ruskin College, Oxford) and BUPA