A lot of kids feel like contaminated goods if grownups don't touch them. Women have more license to touch, quite frankly, because our touch is not held in suspicion, the way a few men have ruined it for all men. But you don't have to put a kid on your lap. They can sit close by and still feel special. It ought to happen as a conversation, and not as a dictum from the administration.
Bullying involves repeated harassment, either physical or verbal, of someone who is weaker.
It can be sexual in nature but it doesn't have to be. But other kinds of bullying aren't necessarily illegal, taunting or name-calling that aren't sexual, for instance. Exclusion is a way of bullying that you see with girls a lot. That isn't sexual harassment, and it's not illegal. But it's a kind of bullying.