Labelling a child a bully doesn't sit well with me. Even labelling an adult a bully seems ill fitting, because to me it almost implies it is a choice that has been made by that individual.
There are too many factors at play in bullying behaviours that being as simple as a behavioural choice is not always the case.
Like all good parenting advice, it is crucial we separate the child from the behaviours - they are not bullies, they are merely displaying bullying behaviours and it is the behaviour we need to address.
In days of old we saw bullying as merely a social learning phenomenon. The children watched the parents and therefore saw name calling, intimidation, teasing, humiliation as the norm. Certainly we see certain family issues at play and parental involvement in the fight against bullying is crucial.
A lack of warmth on the part of parents is as a factor, indeed as is a lack of supervision. This, to me all comes back down to education and explaining behaviours to our children. Social skills and the social emotion of empathy starts at a very early stage, in fact the earliest of stages, first smile, cuddle, interactions.
A child must be addressed for biting, name calling, pushing ahead in the playground, calling someone names etc. When I say addressed, I don't mean discipline. The children are learning and they need guidance. Explain the emotion and the emotive consequence behind a behaviour. If you as parent have no issues with these behaviours, then your child will think they are ok and will bring them into their social world.
Within school, children will bully others because their 'friends' are bullying. I say 'friends' because often it is the social power within a group. In order to maintain their place at the top of the food chain, people will gather a group and this is where children who would never behave like this often start bullying behaviours, especially girls. For teenage girls this is often fun and a great way to alleviate boredom.
The boy or girl at the top of the food chain is maintaining their place of power because they need to address their own issues. Insecurity, bullying at home, bullying in a previous school, fear of isolation. Many issues could lead to an imbalance of social power, which the child needs to address by harming others and raising their social status.
Ultimately, bullying is carried out by those with low emotive empathy, different from cognitive empathy, where they understand the harm they cause, emotive empathy is having the motivation to do something about it. Children under the age of 12 rarely have this level of empathy development and so need constant education on this crucial of life lessons.
In some cases certain traits such as callousness, narcissism will require more intensive interventions.
For the most parts children who bully need to learn appropriate ways to behave and this starts at home. In schools, it will continue if not seen or when seen, it is ignored or dealt with too harshly and without education.