The first priority is to protect the school's image.
We also see this on college campuses with alleged rapes. The first thing a school wants to do is "circle the wagons"
Teachers and administrators meet to determine their messaging statement and ensure no one says or does anything that may leave them open to a lawsuit.
The next step is to evaluate student's individual file history in order to determine which person is most likely to be trustworthy. I imagine the vast majority of bullies will deny bullying anyone or offer a different version of events. There have been incidences where the so called bullied child instigated things and the bullying began as retaliation.
Punishments may vary based upon the type of "bullying", age of the students, and how prominent the parents are in the community.
The ultimate punishment a school can hand out is expulsion. However that is unlikely if you're dealing with pre-teens or Jr. high aged kids unless there is something "extreme". In most cases the punishment is a 3-5 day suspension and a warning not to engage with the victim again.
Historically parents may have opted to pull their child out of that school and enroll them into another. However with today's "social media" bullying can take place 24/7 over the Internet
I imagine the biggest challenge for any parent of a bullied child is to convince them that "today is not forever".
Depression sets in when one lacks hope and or does not believe they have anything to look forward to in life. If at all possible a parent has to counterbalance the effects of bullying by taking their child on vacations, engaging them in fun activities, and other things they may enjoy. Whenever we have a larger view of the world it's easier to put things in perspective and avoid the feeling that the whole world is coming to an end. Bad times never last forever.