ты не прав, вот смотри
Etymology
The word "bully" was first used in the 1530s meaning "sweetheart", applied to either sex, from the Dutch: boel, "lover, brother", probably diminutive of Middle High German: buole, "brother", of uncertain origin (compare with the German buhle "lover"). The meaning deteriorated through the 17th century through "fine fellow", "blusterer", to "harasser of the weak". This may have been as a connecting sense between "lover" and "ruffian" as in "protector of a prostitute", which was one sense of "bully" (though not specifically attested until 1706). The verb "to bully" is first attested in 1710.[20]
In the past, in American culture, the term has been used differently, as an exclamation/exhortation, in particular famously associated with Theodore Roosevelt[21] and continuing to the present in the bully pulpit, Roosevelt's coining and also as faint/deprecating praise ("bully for him").
то есть и пишется иначе (bullying вместо bulling, ибо наше знание языка во всей красе), и корень другой
очень интересно слово изменило значение с "братишка, балагур" до "угнетатель слабых".
я посмотрел всякие сомнительные источники в интернете и там нет единого мнения о том, не было ли это следствием влияния слова bull. То есть, корни разные, а смысловая нагрузка могла быть заимствована из схожего по произношению слова.