Jesus died on the Cross for everyone, bullies included. Perhaps part of His plan is to allow a certain amount of chaos to happen in His house, so we can pray for those who harm us. They are among the poorest of the poor, and they desperately need our prayers. When we are being tormented by someone, our prayers for them possibly become more powerful, since we are also uniting our sufferings with the Crucified Christ.
As Christians, we are called to love everyone, regardless of whether they behave or not. We also want the best for our neighbors, which would be their eternal salvation. We have to believe that God has the power to totally and completely transform them. When they get to Heaven, they will have pure souls and clean hearts. They won't be the same people we know now.
Only God can bring about this type of spiritual healing, because personality disorders that would cause an adult to bully another are pretty fixed. Although psychologists consider malignant narcissism a permanent character flaw, people can and do change. With God's help, anything is possible.