WASHINGTON — Margaret Fiester is no shrinking violet, but she says working for her former boss was a nightmare.

“One day I didn’t do something right and she actually laid her hands on me and got up in my face and started yelling, ‘Why did you do that?”’ said Fiester, who worked as a legal assistant for an attorney.

Fiester doesn’t have to worry about those tirades anymore, but she hears lots of similar stories in her current role as operations manager at the Society for Human Resource Management, where she often fields questions about the growing issue of workplace bullying.

On-the-job bullying can take many forms, from a supervisor’s verbal abuse and threats to cruel comments or relentless teasing by a co-worker. And it could become the next major battleground in employment law as a growing number of states consider legislation that would let workers sue for harassment that causes physical or emotional harm.

“I believe this is the new claim that employers will deal with. This will replace sexual harassment,” said Sharon Parella, a management-side employment lawyer in New York. “People who oppose it say these laws will force people to be polite at work. But you can no longer go to work and act like a beast and get away with it.”

Many companies already recognize workplace bullying as a problem that can sap morale, lead to increased employee turnover and even affect the bottom line. Half the employers in a 2011 survey by the management association reported incidents of bullying in their workplace, and about a fourth of human resource professionals themselves said they had been bullied.

At St. Anthony North Hospital outside of Denver, human resources director Robert Archibold says most of the bullying incidents he sees are peer-to-peer. In a recent case, one worker got offended by a co-worker’s remark and suggested they “take it out to the parking lot.” The offending worker was suspended under the hospital’s anti-bullying policy, which has been in place for more than a decade.

“Hostile work environments, threats, bullying can come from anywhere,” he said. “You can’t tell by looking at someone who it will be.”

One reason the issue has attracted more attention in recent years is that parents who deal with school bullying realize it can happen in the workplace, too.

Some employers have put into place anti-bullying policies, but advocacy groups want to go even further. They have been urging states to give legal rights to workers who do not already fit into a protected class based on race, gender or national origin.

More than a dozen states — including New York and Massachusetts — have considered anti-bullying laws in the past year that would allow litigants to pursue lost wages, benefits and medical expenses and compel employers to prevent an “abusive work environment.”

Gary Namie, a social psychologist who co-founded the Bellingham, Wash.-based Workplace Bullying Institute in 1997, is among those leading the charge, along with labor unions and civil rights groups. He says the economic downturn has made bullying even worse and argues that passage of the laws would give employers more incentive to crack down on bad behavior in the workplace.

“People are trapped; they don’t have the same alternative jobs to jump to,” Namie said. “They are staying longer in these pressured, stress-filled, toxic work environments.”

Business groups have strongly opposed the measures, arguing they would open the floodgates to frivolous lawsuits.

“We would look at a bill like this as overreaching,” said Marc Freedman, executive director of labor law policy for the U.S. Chamber of Commerce. He said the bill would punish an employer for acts of its employees that it may not be able to anticipate.

But Parella, the employment lawyer, thinks it’s only a matter of time before states begin passing these laws and bullying issues become a major factor in workplace litigation.

“Once it passes in a few states, there will be a chain reaction,” she said, noting that other countries such as England, Ireland and Sweden already have laws addressing workplace harassment.

In Massachusetts, the National Association of Government Employees Local 282 has been one the first unions in the country to include an anti-bullying clause in collective bargaining agreements.

“From a labor perspective, we want there to be remedies in place for corrections to be made, not to yell, scream, threaten or treat the person basically like a slave,” said Greg Sorozan, president of NAGE, which represents about 12,000 public employees.

In 2008, Sorozan succeeded in placing “mutual respect” provisions in labor contracts with the state that say harassment, abusive language and bullying behavior will not be tolerated in the workplace. It allows workers to raise concerns with managers and file a grievance if not satisfied.

Sorozan said the provision recently helped workers in a state office who complained about a manager who acted bizarrely, leering at employees over cubicles and randomly punishing those who questioned him by reassigning them or refusing to let them take vacations. After the union complained, the manager was eventually forced out.

The management association survey found that 56 percent of companies have some kind of anti-bullying policy, usually contained in an employee handbook or code of conduct. Most said their response to bullying allegations depends on the circumstances but could include suspension, termination, reassignment or mandatory anger management training.

Employers say the vast majority of bullying incidents are verbal abuse, such as shouting, swearing and name-calling, along with malicious gossip, rumors and lies. Bullying through technology, such as Facebook or other social media, accounted for about 1 in 5 incidents, the survey found.

“It’s usually the manager or senior executive who’s just a complete out-of-control jerk,” Fiester said. “Everyone’s going to be walking around on eggshells around somebody like that. You’re afraid to make mistakes, you’re afraid to speak up, you’re afraid to challenge.”

If the bully is a senior manager or CEO, resolving a complaint can be tricky for a low-level human resources employee.

“It might be a little bit difficult to discipline the CEO,” said Fiester, the human resources adviser. “You are really walking a tightrope.”

She suggests approaching someone else in senior management who might be in a better position to approach the boss.