One of the Disney CM told me that not only do you not "need" carseats on the bus, but in fact it is prohibited by florida law to use car seats on a tour bus. Frankly I don't understand. I have notices that most tourbusses don't have seatbelts, and it always makes me uncomfortable. In anycase, I was told that for Magical Express, carseats are stowed underneath.
A car seat only makes things safer if there is a seat belt to fasten it to the vehicle. If there's no way to fasten it, then the car seat actually becomes a missile rather than a safety feature.
DME motorcoaches are plushly upholstered. Disney Transport buses (the ones you take between the resorts and the parks) are like city buses, only cleaner -- they have hard plastic seats.
If you are not comfortable with your small kids on such transport, your only real option would be renting a car at the airport and using your own car seats at all times.
My wife and I have no problems taking our kids on the buses. We started at WDW when they were 5 and 2.5. Due to our jobs, we see the devastating effects of motor vehicle accidents every day, yet we have no problems with our kids on buses. But on smaller vehicles like a car or van or SUV (where injury due to an accident is MUCH more likely due to the smaller size and lower height of the passenger compartment) we would NEVER allow our kids to ride without the proper safety seats. Without going into the physics of it, buses are overall safer due to their hulking size compared with the other vehicles around. In a typical accident, even if a car rammed into a bus, the frame of the bus absorbs much of the energy, and due to the bus's mass much of the energy keeps the bus moving and doesn't transfer to the passengers much at all.
Weird example: let's compare cars to toddlers and buses to adults. If a toddler runs into another toddler at full speed, there's going to be a lot of crying and perhaps an injury or two. But if a toddler runs into a full-size adult at full speed, the toddler will basically bounce off the adult. The adult might get a little knocked off-balance but won't be knocked over and won't be hurt, because the adult is so much bigger.
ANyway, it's a personal decision, and you have to do what makes you the most comfortable. Just know that there are millions of us who, with our kids, use not only Disney buses but regular everyday city buses as well.