In this day and age, the advice to "ignore the bully" and "don't get into fights" just doesn't work. In fact, it's outright dangerous, because all you're doing when you offer this "advice" is sweeping it under the rug. It is no wonder that suicides and school shootings are so common these days, and the blame is squarely placed on bullying.
On the other hand, martial arts isn't a quick fix, either. It takes years of good martial arts practice to be physically able to handle oneself against the typical school bully.
I have always taught my kids never to start fights, but you have my blessing if you end the fight. Of course, that will usually lead to detentions and suspensions, and so, this is where the adults need to finish the fighting. And when I mean adults, I'm referring to bullied's parents, bully's parents teachers, police, child protection services, and lawyers. School administration does not respond well to parents. You get their attention when lawyers get involved. So that's what you do. March into the administration's offices with a very loud mouth, and the will to back up any threat to bring in lawyers. Or have the lawyers do the talking.
I wrote an extensive how-to in this question:
Martial arts to intimidate school bullies
Martial arts wasn't going to help the questioner then, it would take a long time to get proficient enough to be helpful. Nevertheless, you are stuck with "the system", so, use "the system". You're a taxpayer. Make your taxes work: you pay for the school, you pay for the police department, your child's rights to self-defense are usurped by the system.
If you ignore the problem, or let someone else deal with it, you are telling your child you just don't want to get involved, and that you don't care. That in itself will undo any self-confidence gains earned in martial arts (or sports or other avenues of building confidence). You are responsible for their safety, and if you hide the effects, but don't address the cause, then the effects will manifest in other ways: substance abuse, truancy, depression, running away, cutting, turning the victim into a bully, behavioral problems at home, suicide, and violent retaliation.
I have never subscribed to the edict that "fighting isn't the answer". That is too naive. It doesn't consider each situation. Fighting may not be THE answer, but it may be necessary. When a gang of kids (see countless YouTube videos) attack a victim, and the victim can't fight back, there could result YEARS of needed therapy, and if not tended to properly, then said side effects of substance abuse, truancy, depression, etc will likely result.