Joe is the worst. Nobody likes him, not even the so-called friends he teams up with at school, filling other students with terror. He's sarcastic, nasty, and a bit of a racist, and especially anti-Semitic. Over-all jerk.
When some of the other kids plan a boat outing just for the kids with Jewish ancestry, he sneaks on board and hides. And crud ends up stranded in Ancient Egypt with them.
My critique group tells me that I've done a good job setting him up with all of the above. It's obvious that the other kids can't stand him and that he's not too keen on them either. In my first chapter with him as a viewpoint character, he generally mentions hitting other kids, but we haven't seen him be violent.
In the school scenes before the time travel, everyone dreads seeing the 3 bully boys. They derail conversations and are overall jerks. But I also want kids to fear them, especially the younger kids (ages 8-11-ish...the school is K-8...meaning ages 5-15, the years before high school).
When Joe's in Egypt, everyone from modern times gives him a wide berth. But not wide enough that they're safe from his words. They just want to be safe from his fists (or feet or whatever). Turns out Joe has a soft spot for toddlers and befriends the time-traveling 2 year old. I want her siblings to be genuinely fearful at first that he might harm her.
Once Joe is in Egypt he discovers he has an opportunity for a fresh start. The local adults respect him because he works hard (he likes physical work, not school). He also makes his first real friend. He's not going to screw this up. He's still somewhat mean and definitely sarcastic, but not outright violent.
I don't want to resort to the trope of bully walks quickly down the school hallway, (not so) randomly shoving kids hard into lockers. That may be what movie and TV makers think is necessary but it's not really how school violence happens. It also takes very little. One quick painful episode a month is enough to traumatize a bully's victim (especially if the timing and action is random).
How do I show that the bully trio, including Joe, engage in physical bullying without it rising to the level of adults or police intervening or TV stereotypes about bullying? But enough that smaller kids are legitimately afraid. Small amounts could be in Egypt.
Note: The kids come from a small town (one primary school, one secondary school) in rural Arizona, USA. The year is 1995, so no cyber-bullying, social media, etc. Bullying isn't completely ignored like it was in my day but awareness of it among adults is meh, not like today.