Bullies are people who abuse smaller/less powerful children. In Operation: M.A.T.A.D.O.R. and Operation: B.R.E.A.K.U.P., the bullies appear to be a semi-formal group led by Ernest. In Operation: E.L.E.C.T.I.O.N.S they are seen siding with The Delightful Children from Down the Lane and The Six-Gum Gang, serving as guards in Permanent Detention.
Numbuh 4 is known to be somewhat of a bully, and has associated himself with Ernest and his group in the past. Bullies are apparently an ancient species, as Jerry Rassic found them on his prehistoric Bully Island.