pick on, tease or bully?

This is a matter of perspective.

If the boy is doing what he's doing because he likes a girl, then he probably thinks he's teasing her.

If the girl is crying, she's probably feeling picked on or bullied.

Primitive flirting.

To me, "pick on" means someone says or does something to another person which is a bit mean, and might cause embarrassment, but would probably not cause a lot of emotional pain.

I use "tease" when one person is saying or doing something to another in a friendly or affectionate way (even if its putting a caterpillar in a girl's pencil case).

"Bully," though, implies that one person wants to hurt another person's feelings, or make him/her afraid. Sometimes bullying can be physical--pushing, hitting, pinching, punching, tripping.