The findings emerged after a series of events to mark last week's Respecting Others campaign. There were around 4,864 calls from youngsters to children's charity ChildLine's Welsh helpline about bullying in 2004-5.
The Cardiff academics graded schools' policies against a series of criteria, including how well they defined bullying, whether they specified different types (such as verbal or physical), and if they set out procedures for dealing with incidents and involving pupils.
Two-thirds were graded at least satisfactory and nearly a quarter were good or outstanding, with the strongest policies integrating anti-bullying initiatives into wider school activities. However, the Cardiff team concludes there is "a great deal of work still to be done", with improvements possible to a third of policies.
"Most commonly, this was where policies had been adopted from a generic template, with little evidence of customisation."
It recommends that schools and governing bodies should assess their policies against the findings, and that local education authority officers are offered a day's training. Schools with weak policies will need LEA support, they add.
Jane Davidson, minister for education and lifelong learning, told Assembly members she was concerned that one-third of schools had not got their policies right. Regarding mobile phone text abuse, she said: "We are looking at all kinds of bullying and need strategies to deal with them."
Howell's school, Cardiff and Charlotte Church correction page 2