I would definitely use the car seat on the shuttle if it's a passenger van. Most states have laws mandating that children be in the proper car seats or boosters in these kinds of passenger vans. NHTSA issued reports a few years ago about the serious safety risks with these vans, so a lot of states classified them like cars- i.e. the same carseat and booster laws apply to the van.
The true buses are a different story. As previously noted, you will not be permitted to use a carseat on DME. I don't know if this has come up with the regular Disney transport buses for the parks, but most cities use this style bus and most cities prohibit the use of carseats on such buses. Most of these buses aren't really equipped to accomodate a carseat anyways.