A third of these said they planned to quit the NHS because of their ordeal.
The problem was worse for minority groups - nearly a third of nurses from ethnic minorities and 41% with a disability said they had faced workplace bullying.
Nearly 30% of agency nurses said they had been bullied.
Over half the nurses who had been victims of bullying said they were not happy with the way the issue was dealt with by managers.
And 38% said that there had been no action taken even though they had reported a case of bullying. Disciplinary action was only taken in 5% of cases.
The Royal College of Nursing (RCN) said a cultural change is needed to make sure nurses get more support.
Stop bullying
RCN general secretary Christine Hancock said: "Bullying is a form of violence that employers have a responsibility to stop.
"Nurses need to be able to work free from fear and intimidation - no nurse can deliver good patient care if they are experiencing harassment at work."
The RCN, which interviewed more than 6,000 nurses for the study, has produced a good practice guide, urging all hospital managers to have a written policy on tackling bullying and harassment at work.
They also give advice on action for staff and nurses to take, the legal frameworks and support available for nurses and training opportunities.
Verity Lewis, RCN employment adviser said nurses need to know they have support.
'Duty'
"It is vital that individual nurses feel confident that they will be properly supported when they stand up to unacceptable behaviour."
The Department of Health said bullying and harassment would not be tolerated.
"Bullying and harassment makes work intolerable for many and is unacceptable in whatever form it may take.
"Employers have a duty to ensure that their staff have a safe and healthy place to work.
"The cost of stress induced by bullying and harassment can involve high levels of sickness absence, accidents, errors, low morale and poor performance."