I wish I'd seen this before now so I could have responded sooner. I am a certified Child Passenger Safety Technician (carseat tech).
The Magical Express buses do not have seat belts. Rather than using restraints to protect passengers, they use compartmentalization. Basically, this means that in an accident, the tall, cushy seats will contain occupants within their seating "compartments" to prevent serious injury. This, along with the size/weight of the buses, provides protection. You do not use carseats/booster seats on them.
I have no problems transporting my children on the ME buses.