The problem emerged after the union carried out a survey of overtime working.
'Staff were building up a lot of overtime and flexitime but were unable to take time off in lieu,' said Unison branch secretary Howard Young.
He said employees felt bullied into working longer and longer hours.
Last November Dumfries and Galloway published a code of practice for staff which said managers must discourage harassment and make it clear to staff what is unacceptable conduct.
A spokesman denied bullying was widespread. But he said the council would be interested in the results of the survey.