We checked our own carseats and it really wasn't that big of a pain, especially if you rent a luggage cart at the airport or can do a curbside check-in.
I personally am not comfortable having my children riding without proper safety seats, especially on busy CA freeways. Our family was involved in a fairly serious car accident and while we were wearing our seatbelts, we were still injured. Our children, thankfully, were left with only minor bruising from their harness straps. I hate to think of what could have happened had they not been properly restrained in their carseats at the time.
I hope that you can find a shuttle company/driver that will work for you. I also suggest that you ask them for the history of the carseats as well - make sure they haven't been recalled or are expired and find out if they have ever been involved in an accident (a lot of people do not realize that carseats should be replaced after an accident). I am not sure what the CA seatbelt law is exactly, but I personally felt more secure having my children in their own carseat and booster for this reason.
While I know that most school buses do not have safety restraints (although I wish that they did), I don't consider that to be a fair comparison to the airport shuttles I have been on, which are more like vans than actual buses. Vans and buses are designed differently and it seems like vans might have a higher rate of roll-overs in high speed accidents.