Since they are an interstate operation, I would think that cooperation with federal law enforcement would be required by the Federal Motor Carrier Safety Administration.
Nevertheless if there is probable cause /reasonable suspicion a warrant should be obtained. the bus in question should be detained while the warrant is obtained. Under these circumstances passengers would not be allowed to exit the bus except within an exclusionary zone which is supplied with porta potties, water and food. Air conditioning (except for the ill) is not a necessity though heat is. As gas is supplied by the carrier to the individual buses, refueling would not be allowed as it would violate the exclusionary zone. Average passengers are going to get really uncomfortable when the A/C cuts off from lack of fuel.
The driver also has a commercial driver's license. Were he or she knowingly allow illegal aliens to travel (illegally), it should be relatively easy to have that CDL suspended. Just sayin ...