Yes. You can, and you should.
Your parking lot and bus loop are not public streets; they are non-public places of learning. This is important because it clarifies the meaning of "public space" and gives district staff the legal standing to enforce that boundary.
If you or your staff see marked or unmarked SUVs idling in your drop-off lane, don't just watch it. Go out there. Don't be rude, but tell them firmly: "You are on school property. You are disrupting the education of minors. If you do not have a judicial warrant signed by a judge, I am asking you to move your operation off school grounds."
If they refuse, you retreat, lock the doors, and document the trespassing. The goal is to make them explicitly refuse a lawful order. That refusal changes the legal standing of the encounter and creates the documentation you need.
