Responsibilities of a workplace bullying?

Not exactly sure what you are asking, but I suggest this is a start to a very widespread and intense problem all over the world:

As a target of schoolyard bullying in my youth, I learned the only way to deal with bullies was to challenge them. Only after demonstrating a willingness to defend myself could a meaningful relationship begin. Sadly, little has changed in going from the schoolyard to the workplace, except in the latter the stakes are higher and there is broad collateral damage. In the case of workplace bullying, prevention makes for better working relationships, greater productivity, happier employees who consequently require less healthcare for stress-related ailments. Prompt identification and correction of bullying prevents the damages associated with unchecked and potentially escalating patterns of abuse, and therby reduce institutional losses and liabilities.

In order to realize the full potential of our society, especially the call to innovation and social justice which enables employees to be at their best, we must proactively maintain and enhance a workplace culture and environment that preclude workplace bullying in no uncertain terms.

Here's a good definition of workplace bullying:

Bullying is unwelcome behavior, whether or not based on a protected classification, that is sufficiently severe or pervasive to create an intimidating, hostile, or offensive environment for employment.

The US Supreme Court acknowledges that the intangible workplace environment is part of the employment contract. See

http://www.eeoc.gov/policy/docs/retal.html

Therefore, if a workplace bully compromises the workplace environment as described above, it may constitute breach of contract, so you can challenge the company itself for allowing it. Of course, you have to document your reasons in terms recognized by your company's policies and the law.

So, the best way to challenge the bully is by exposing their misconduct through formal disclosure to the proper authorities. But try not to get involved in formal grievances, as they involve tedious procedures that often involve confidentiality, precisely what you want to avoid. You want everyone to know what's going on and that's not acceptable under policy or law because its a breach of contract. Also, they have higher standards of evidence to prove than disclosure of alleged wrongful conduct. In disclosure, so long as you don't knowingly disclose false allegations, and you make your allegations in good faith, its enough to require a response. That is:

In regard to Hagan v. Echostar Satellite, No. 07-20191, 5th Cir., 2008, it is reported (http://www.thehrspecialist.com/8237/Federal_court_clarifies_Protected_activity_under_the_FLSA.hr?cat=employment_law&sub_cat=flsa):
In regard to Chial v. Sprint/United Management Company, No. 08-2012 (8th Cir. 2009), it is reported (http://www.lexology.com/library/detail.aspx?g=a99aaa99-8154-462c-b14d-e710c7b51a02):