I have to respectfully disagree with 44brendan. I have worked as an employee advocate and been involved with many employment unions, from the employee and employee advocacy side...
Human Resources #1 job is to protect the company, not the worker. They are mainly interested in cleaning up messes to make the company and the management look good. They will side with the company 100% no matter what, unless the evidence against the company is strong enough to precipitate a lawsuit. They will only act in the employee's behalf if they know there will be a lawsuit and they will lose.
bullying is common and hard to prove. Finding a new job is the best solution. I know this is probably not what you want to hear, but I hope it helps you somehow. I have seen these situations unfold firsthand.