Don’t lose faith just because your bully lied and people seemed to believe them. Keep doing what you need to do and keep applying pressure on them to stop. Consistent, compassionate pressure.
When someone is accused of bullying, our biases impact how we respond to the allegation. In fact, they impact whether we believe the allegation or not.
It is a huge mistake to characterize a kid who is behaving badly and bullying as evil. First, it gives them more power over our imaginations then is warranted. And second, it prevents us from doing what we should be doing to stop them.
Their goal is rarely against a particular group of people (though they might justify their behavior that way). The goal is social exclusion and power. Until and unless we deal with that, as the goal, we will fail to get it to stop.