In an NHS staff survey at East Kent Hospitals NHS Foundation Trust, 42% of staff said they were targeted in 2014.
The trust, which runs hospitals in Ashford, Canterbury, Margate, Dover, is in special measures.
It said it had done work to address the issues found by the survey and identified by the health watchdog.
The number of staff who said they were bullied has risen from 31% in 2013.
It was put into special measures last September because of "serious failures" in patient safety.
The trust runs the William Harvey Hospital in Ashford; the Kent and Canterbury in Canterbury; the Queen Elizabeth the Queen Mother (QEQM) in Margate; the Buckland in Dover; and the Royal Victoria in Folkestone.
Sandra Le Blanc, director of human resources at the trust, said: "The questionnaires were completed... a matter of weeks after the trust was put into special measures following the publication of the Care Quality Commission's (CQC) report.
"The results [of the survey] reflect where we were then as a trust, because bullying was identified as an issue in the CQC report," she said.
"We've done quite a lot of work since then to address some of the issues raised in the report."
She said a confidential phone line was set up for staff following the report and managers were putting in a programme of "good working practices".
Ms Le Blanc said she was unable to comment on why the number of staff reported being bullied had risen from 31% in 2013 to 42% in 2014.
"Bullying is a very complex issue. It's not just about the managers, it's also about staff's behaviours with other staff."
More than 40% of staff at a Kent NHS trust were victims of harassment, bullying or abuse by colleagues, figures show.