Bullying is very hard to define. After all, one person's bullying might be another's natural rough and tumble of school life. Generally though it covers :
Physical. Pushing, kicking, hitting, pinching and other forms of violence or threats.
Verbal. Name-calling, sarcasm, spreading rumors, persistent teasing.
Emotional. Excluding (sending to Coventry), tormenting, ridicule, humiliation.
Racist. Racial taunts, graffiti, gestures.
Sexual. Unwanted physical contact or abusive comments.
Homophobic. Any hostile or offensive action against lesbians, gay males or bisexuals or those perceived to be lesbian, gay or bisexual.
I think the point at which it becomes bullying though depends on how it affects the target. Some children just manage to shrug off name-calling, pushing and shoving, etc., but others find it intimidating and frightening.
You need to judge really how your child feels about all this. Some children will find your intervention embarrassing, if the incidents are minor or part of the general relationship between the two involved. For instance, kicking and punching might be as a result of the "victim" shoving the "bully" or calling them names.
If the behaviour appears to be taking on a pattern which looks as though it might set the form for their future relationship, or escalate into something more, then you do need to nip it in the bud. I do think, though, that sometimes jumping in with accusations of bullying can make a mountain out of a molehill - and this is someone who has had to deal with her son being badly bullied recently, so I am not in any way trivialising or dismissing what is happening.
Perhaps just a gentle word with your child's teacher to alert her to what is happening will be enough to focus attention on the relationship.