Do you know how to handle bullying?

but we don't see much beating or hitting.

Almost 30% of youth in the United States (or over 5.7 million) are estimated to be involved in bullying as either a bully, a target of bullying, or both. In a recent national survey of students in grades 6-10, 13% reported bullying others, 11% reported being the target of bullies, and another 6% said that they bullied others and were bullied themselves.[1

I posit that personal self confidence (not really arrogance but that'll do in a pinch) is the vital component.

Absolutely. An appearance of self-confidence is key. I know of any number of cases where bullies wouldn't approach a prospective 'mark' simply because it looked like it might be too much trouble. It's all in how you present yourself.

•Bully-victims reported the most child maltreatment (44%), which included experiences with physical and psychological abuse and neglect.
•Bully-victims also reported the highest rates of sexual victimization (32%), which included experiences with sexual harassment as well as sexual abuse, and included familial and non-familial perpetrators.
•Bully-victims and bullies witnessed higher levels of victimization within their homes (e.g., domestic violence) and communities (e.g., witnessing attacks) than other youth (59% for bully-victims, 61% for bullies).

A significant link between bullying and victimization patterns at home and at school was found. Children who bullied siblings were likely to bully their peers, while victims at home were likely to also be victimized at school. Dr Menesini continued: "It is not possible to tell from our study which behaviour comes first, but it is likely that if children behave in a certain way at home, bullying a sibling for instance, if this behaviour goes unchecked they may take this behaviour into school." In conclusion this study gives immediate implications for interventions. In order to prevent and reduce sibling bullying, parents should attend to sibling relationships and attempt to mediate and reduce high levels of conflict, especially if they have older sons and if the sibling relationship appears negative and highly hostile

My doubt is that any two administrators would agree on any kind of rules, much less a whole district.

Except when we're talking emotional bullying, especially the kind girls typically practice. Getting another girl to physically attack when goaded would be GOLD to the kind of girl I'm thinking of. That would be the mark of success, even if it hurt like hell. Because the trick would be to lay groundwork and the goad with something that didn't even seem that bad to onlookers, and then the attacker would be ostracized for "unprovoked" violence.

In the kind of situation I'm thinking of, no response is far better than a violent response. That's not from an adult, do-the-right-thing perspective, its from a utilitarian perspective. It'd be counterproductive for the bullied kid in that kind of situation.