I was bullied mercilessly as a child and I think that was mostly because my parents’ advice was to “just ignore it; she/he is jealous of you.” That advice doesn’t really help much, IME.
My parents also did not go to the school and talk to the teachers or administration, or the bus driver, which is where a lot of bullying happens. I suspect that would have made it worse.
My advice is to teach your kid how to set limits and stand up for herself. Don’t teach her kickboxing or go over the top with that. She doesn’t want to become the bigger bully; that’s not the goal. But, in general, in my experience, bullies bully because they have exceedingly low self-esteem, may be abused or neglected at home, and have to pick one someone they perceive to be smaller and weaker in order to feel better about themselves. Also, bullies are, as a general rule of thumb, cowards.
So here’s a little anecdote about how I handled a situation once in high school. Take whatever gems of wisdom from this that you choose.
So we’re talking about 9th grade gym class – the only class that wasn’t really divided by “college track” vs. “fast food track.” Right? So everyone in the gym class was from different socioeconomic backgrounds and fit into different demographic categories. A very mixed crowd. (Don’t flame me for this next, please, the race of the individuals involved is relevant to the story.)
So the school was about 60% black/40% white. The gym class happened to be about 80% black/20% white. It was winter in the Midwest, so all gym activities had to occur inside. This particular unit was “jazzercise.” Yes, this was in the 80s, so sue me, I’m old. The lazy teacher had trouble controlling the class because she had some troublemaker/rabble rouser punk girls in there who were always very disruptive (in any class) and pretty much took control and ran things they way they wanted to. So the teacher threw her hands up and told us to pick out whatever music we wanted, divide ourselves into groups, and each group was to come up with our own jazzercise routine, which of course, turned into a dance competition.
I was one of four white girls in the class, and all four of us were geeky, dorky, smartypants types. Not one of us had a lick of rhythm. However, I had (and still have) a deep and abiding love for music so I picked one of my favorite songs at the time, which was Erotic City by Prince. Yes, I was only about 13 at the time. 
So we start playing our music and trying to come up with some moves, we four dorky, awkward white girls. This large, tough, semi-punk black girl stalks over to my little group and gets right up in my grill, all threatening and menacing-like. She says, “I know you don’t even have any moves. You got no bidness using that music!” I might have even gotten a finger in the face and a good head-waggle to boot.
Now, I’m sure I was supposed to “throw down” which means I was supposed to defend my honor and fight this chick, who would have wiped the gym mat with me in two seconds flat. So I agreed that I had no moves at all and would she be willing to teach our group a few moves so we wouldn’t look so stupid when the teacher graded us?
Turned the whole situation around. Instead of responding to the bait, I asked the girl for her help. That bolstered her self-image enough (She was valuable! I needed her help!) so that she brightened up, called her friend-girls over and said, “Now we gotta teach these white girls some moves so they don’t embarrass themselves.” Half of my high school’s Ladies Basketball Team descended upon us and taught us how to move our hips so that it looked like we had more than a couple vertebrae and that’s how I learned rhythm. I ended up having a passing acquaintance/friendship with that girl and her basketball team, but she never asked me for help with academic stuff, although I’d have been happy to return the favor if she had.
I was never bullied again. Lesson: You can stand up to someone without inflicting violence yourself, or inciting a fight or a race war in your gym class.