Bully is shown to have very spiteful behavior and is usually seen picking on students.
He is extremely tenacious and can be a real pest to kids like Jeffy. He is also not the brightest since he keeps on picking on Jeffy despite having been beat up plenty of times and in "The Fight!", he doesn't know his ABC's, having to cheat to say the letters in the correct order.
He also has a hugely hostile relation with almost everyone in his class (with the exception of Patrick and Penelope despite still sometimes being mean to her, they have a mostly neutral or positive relationship). His relationships with less prominent students (like Todd) are unknown.
He revealed that his parents are never there for him, which is why he bullies people.
Speaking style
Speaks in short, sharp sentences with a taunting cadence; often sneers and uses exaggerated confidence to mask insecurity