Bullying is a vile behaviour. It's systematic and ongoing and some people can be quick to use the term inappropriately after an isolated incident or petty fall out.
Generally children should develop the social skill to deal with most routine issues themselves. They should also know when it's appropriate to seek support from an appropriate adult.
Bullies like an easy target. I was small, uncool, happy enough in my own company and had to take the bus home on my own. Some girls from the year below me made the error of thinking I was an easy target... first they tried comments. I either came out with something deeply witty or intelligent as a put down. I was confident enough not to give a toss about what they thought of me. If I couldn't think of something to say, I'd ignore them, fixing my gaze through them as though they werent there. They found that disconcerting. One day they upped their game, getting me alone at the bus stop, leaning on my deeply uncool, battered sports bag trying to innocuously pull me to the ground. They were looking at each other trying to look innocent rather than paying attention to me. I took advantage and gently unhooked the shoulder strap, letting the bag drop under its own weight and letting the handles drop into my other hand. The girl fell over as I'd hoped, and also got a bonus whack in the nose from the metal buckle as it swung up
As she picked herself up, they demanded "what did you do that for?" I said "you deserved it". Fortunately the bus then pulled up and I got on it before they worked out what to do. They never went near me again 
I couldn't change the fact that they had a range of victims to pick on. I could make myself an unsatisfying target.
I don't want my children to be violent, but I want them to have the confidence to defend themselves when someone repeatedly refuses their requests to be left to be in peace. They are still young and beginning to squabble. I try to find out the cause of their spats, and tend to be more cross with the one being repeatedly annoying in the first place rather than the one that lashed out in frustration at the behaviour of the first when their requests have been ignored.