If the bully encouraged such said kid, gave him ways to do it, and continued to threaten him when it wasn't done, then yes.In that case should a bully be charged with murder if a kid killed himself because of that?
They should be charged with involuntary manslaugther.
Involuntary manslaughter occurs when the agent has no intention (mens rea) of committing murder, but caused the death of another through recklessness or criminal negligence.The crime of involuntary manslaughter can be subdivided into two main categories: constructive manslaughter and gross negligence manslaughter.
I believe she fits the bill of constructive manslaughter