Two weeks after the arrest of a 13-year-old girl over the assault of another teenager at a school on the New South Wales south coast, a family has shared how their daughter's suicide attempt forced her to leave the same school.

It comes as an anti-bullying campaign petitions the NSW Government to create legislation imposing harsher penalties on school bullies.

For Jessie, a former student at the school in Bega, the footage that circulated on social media of a 13-year-old girl being pushed down a stairwell and attacked by a fellow student was just another example of the school not intervening to stamp out bullying in the early stages.

The 15-year-old left the school earlier this year because she felt unsafe and unsupported when she was being severely bullied, at school and online, by a classmate.

"There were a lot of messages saying I should kill myself and I didn't deserve to have any friends," Jessie said.

A Snapchat message sent to Jessie from a fellow student. ( Supplied )

She dropped out of the netball team and left a part-time job to escape her tormentor, before finally changing schools a few months ago.

Jessie's family said the school failed to take appropriate action after a senior teacher was shown messages sent using the social network Snapchat.

One message said: "You honestly can't believe anyone likes you. Just die — I'm more than happy to help you out with that."

"I was really disappointed that she [the teacher] didn't do anything … [it] was as if she really didn't care," Jessie said.

"Another part of me felt that everything [the classmate] was saying was true and the only way I was going to get out of it was to end my life."

Children being 'tormented' at school

Anti-bullying advocate Mel Graham's daughter Jessica suicided in 2015 after years of bullying. ( ABC News: Chloe Hart )

Anti-bullying campaigner Mel Graham said thousands of Australian families are equally frustrated by the way state schools are handling cyber bullying.

Mel and Dave Graham's 14-year-old daughter — who was also called Jessica — took her own life in 2015.

She had anxiety and depression, triggered by years of bullying.

"Kids are getting tormented at a school that us as parents have to send our kids to," Ms Graham said.

"But the education department isn't doing their duty of care and actually keeping kids safe."

However, one of Australia's leading experts on teenage bullying behaviour said parents might be surprised how much schools were doing behind the scenes.

Associate Professor Barbara Spears from the University of South Australia's School of Education said relationships between 14-year-old girls could produce some "nasty stuff" and the challenge for schools was keeping up with technology and students' evolving maturity.

"What they are dealing with is a change of population and change in social cultural and technological morays around them," Ms Spears said.

She said it was important for the families of both the bully and the victim to be involved in open discussions with the school.

'We got nowhere'

In Jessie's situation at Bega, her parents said the school's attitude made them feel as if they were causing a problem.

They were told to drive their daughter to school to avoid the bully on the school bus.

"We just got nowhere," Jessie's father Peter said.

"The school tried to keep Jess separated, which was only bringing her down.

"She was stuck in a room on her own half the time, [she] can't go hang with her other friends … [it] only made the situation worse.

"The bully wins and the system does nothing."

Ms Graham said she has talked to hundreds of parents around the country who are all facing situations where their bullied child was isolated as a result of the school's approach.

"They take them out of their classes and put them in a library with one-on-one teaching," she said.

"The victims are the ones getting isolated from the classrooms, from the social scene, from the fun of school."

The Grahams are behind a campaign to get the Government to introduce "Jessica's Law" — a proposed amendment to the NSW Crimes Act, which would ensure all schools take a tougher approach to bullying.

Supporters are following the lead of parents in other states who say they are desperate to protect their teenagers against cyber bullying.

New laws could be counter-productive

In South Australia, Libby's Law was considered by parliament before the recent state election.

It was modelled on Brodie's Law, introduced in Victoria in 2011, following the suicide of young waitress Brodie Panlock.

But Professor Spears said mandating change could be counter-productive.

"It may be a tick the box and that's not really going to help the relationships," she said.

All schools are responsible to the National Safe Schools Framework — an overarching policy that forms the basis for dealing with behavioural management, anti-bullying, social and wellbeing policies.

"They don't have to sign off on it, but actually have to have policies, and they do have to respond to keeping children safe."

A spokesperson from the Department of Education and the Bega school said public schools were leaders in anti-bullying and conduct a range of activities "to encourage respectful, positive relationships".

"Public schools actively support students who have concerns about issues, including bullying, even if that concern arises from outside the school," the spokesperson said.

"That support may also involve a student's parents.

"In some instances, schools recommend parents seeking the support of police or other agencies, such as the eSafety Commissioner, when it appears an activity may be unlawful or the agency has powers beyond the school."