If someone is depressed because they are being bullied, there are plenty of outside resources available to them so that they can get help. If they can't turn to their family or other adult for help, there is also the National Suicide Prevention hotline. In addition, many states have passed anti-bullying legislation, so if a situation is so bad that one is contemplating ending their life over it, they can also contact the police, as odds are there are laws that are being violated and they will be able to step in and help as well.
If the bullying is occurring at school you can also contact a guidance counselor, teacher, up to the district superintendent for help if needed. There are so many options available for assistance, that there is really no reason for anyone to have to choose ending their life over it.
Many people commit suicide not because they want to die, rather they just want the pain they are in to stop. So if you say someone kills themselves because of bullying they are to blame. I would say they made the decision to die, but others pushed them to that decision.
People who bully others are in pain themselves and just want others to feel pain too. Always stick up for people who are being bullied. Most bullies choose the most vulnerable and defenseless targets they can find which shows you how weak they really are. Bullies have to make others feel pain to make themselves feel better.