Long time ago, I found a good word about bullying. It is not ĉagreni because it is longer, but it is not turmenti because it is milder. I would like to find the word and to adapt it to mean "school bullying", and then adapt it again to mean "school bully".
I think the best way to capture “to bully” is the verb ĉikan·i. PIV defines it as:
Intence fari al iu maljustajn ĝenojn, malagrablaĵojn, malhelpojn, por sentigi al li/ŝi sian superecon.
So “a bully” would be ĉikan·ant·o, if it's a person who was bullying in a moment we're talking about, or ĉikan·ul·o, if it's a person who often bullies other people. The noun “bullying” would be ĉikan·ad·o, which is the translation used in the Esperanto Wikipedia.