If the school bus is owned by the system, then it should have the name of the school on the side (like Plano ISD). The leased busses will usually (I say usually) not have that on them. I have seen brand new busses being transported from the factory and they already have School Bus emblazoned on them. Additionally, old busses that have been sold to private tubing companies, churches, etc will still have that on them many times.
Another scenario is one that there is no wording on it, but is being used by the school. My daughter went to state competition for theater. The theater teacher had to rent a truck to haul props down to Austin. That vehicle now fits the statute as it is being paid for and used by a school, so would be off limits period.
The gray area I can see is if a school leases or loans a bus to be used for some non-school event. If the bus driver is being paid by the school or the school is getting no money, then I would say it would be off limits. If they school leased it to a private party and the party was paying all the expenses, then I would say it was NOT a school vehicle any longer and you would be able to carry unless oral or posted notice was given. The first situation may happen at times, but would bet it is rare as I can't see the school wanting the liability for other activities other than school functions being conducted with their vehicles.
Bottom line, unless it is under the control of the school from a manpower or $$$ standpoint at the time, then I am going to assume it is NOT a school vehicle and will carry unless prohibited otherwise.
I reiterate, IANAL, but I used to play softball with a bunch of them.
