I contacted Super Shuttle and the Airport Bus. The gal who wrote from Super Shuttle said, yes, they do require boosters. The bus said no, they don't even have restraints in them so there's no use for a booster.
You should contact them yourself, then take a copy of the e-mail along in case they question you.
I'm keeping my options open on transportation. Depending on how tired the kids are and whether we're on time, we could do either of those, or taxi. I've had a lot of people suggest taxi, so I'm leaning that way. It's about the same price as the Shuttle for our family.
I went to Target and bought the booster that is just a seat and arm rests. My son just turned 4, but he's as big or bigger than many 6 year olds, so the belt fits him fine without a guide. The booster was $17. It has pull-out soda holders on the side, which is a good thing for the car.
It seemed a waste to buy a new booster when I already have two of the high-backed style. But, I figure this is one he can use until he's ready to move out of a booster altogether...and since it weighs about 3 lbs and can even fit inside a suitcase with no problem if I decide to do it that way on the flight home, I decided to go for it!