Sources on the early years of Mussolini - as happens with other prominent figures of the 20th century - are quite sparse and in general suffer from the usual problems with aneddotical evidence.

I will go through what I know about it.

Mussolini was born in a relatively poor family - they had enough to eat but could only afford to have some meat on sundays - in the italian region Romagna, at the time famous not for seaside vacation but for agriculture. His father was a locally relevant political figure.

He started school in Predappio in 1889 and, according to his own words:

I was a quarrelsome, restless brat. Often going back home with my head broken [as in injured] by a stone. But I knew how to get back at them. ... I brought to mischief many of my coetaneous. I was the leader of a small gang, running wild along the streets, rivers and country fields.

De Begnac wrote about the same years:

His violence and his will of dominance forced him to fight. ... Soon he became acquainted with the blood of others - and his own

Despite his attitude, he was a smart boy and inn 1892 his mother sent him to a boarding school held by Salesian Fathers, in the town of Faenza. There he met the strong discipline and strict rules of the fathers.

He hated the place - he often remarked how he despised the fact that he was forced to eat his supper at the poor boys' table (the school had three classes of tables).

In 1894 an incident occurred, where he wounded a schoolmate's hand with a pen-knife.

I was taken to the closet of the theater room [and left there] ... It was night already when I heard someone coming. ... The master told me: "You will sleep with the guard dogs tonight" [I tried to go back to my room] but the dogs barking sent me back. When the dogs left I ran through the courtyard but the gate was locked. I shaked it but to no avail. The noise called back the dogs. ... I climbed the gate and managed to get by, not without leaving a shred of my pants in the dog's bite... Three days later I was sentenced to the following: going back from 4th class to the 2nd, being placed in the corner until the end of the year and eight days of seclusion.

After the incident, he was sent to Forlimpopoli where he attended a secular boarding school, held by Valfredo Carducci (Giosuè's brother). He remained there until 1901 and his behaviour improved; also his marks were good and he was able to complete his course of studies.

In 1898 another incident occurred that forced him to attend lessons in the following to years as an external student. Yet, despite his attitude, his personality appears to have been appreciated. We know for example that V. Carducci picked him to speak at a function held in the boarding school to commemorate Giuseppe Verdi in 1901.

As you can see - while it is clear that Mussolini wasn't a quiet peaceful kid - the definition af a bully appears questionable.

The major sources treat these episodes as signs of a personality looking for self-affirmation; they appear to see nothing wrong with them and he is depicted as a troubled but not bad natured kid. Inlcine to violence but never mean or cruel.

Unfortunately the major sources are not especially reliable, given the apologetic nature of De Begnac's work or the fact that most of the interviews were taken after 1922.

At the same time the narrative of violent Mussolini, who was mean and tyrannical even as a kid is a product of treating mere fun-facts as evidence in a simplistic personality characterization; quite common after the end of the war.

It must be noted that a very troubled kid would have had a hard time finishing his studies - especially one coming from the lower classes. Also Mussolini was later able to became - if shortly - a school teacher himself.

With this in mind - and the understanding that Mussolini would have rather appered violent than weak in the time when his early years became subject of interest - it appears to me reasonable to conclude that his violent behaviour was within the borders of what in those years could be described as a normal child.