i found out how to do this by accident when playing bully last night.
first thing you do is choose the kid you plan to bully i always bully pedro and sheldonbut i think it will work for any kid.
once you have selected your target equip the stink bombs and throw one at the kid then switch to either the bottle rocket launcher or the potato gun
while the child is choking on the stink bomb shoot them.
the kid will end up on the ground and the prefects will be none the wiser to continue shooting the kid just throw a stink bomb first and then shoot the kid.
this only works with the bottle rocket launcher and the potato gun using the slingshot and firecrackers or kicking the kid when it is on the ground will make the prefects come after you.
i haven't tried using the eggs yet so i don't know if they work