I've always used ADO... you get on the bus right outside the airport (literally walk out the exit, turn right, the buses are right there) and the bus station in Playa is two blocks from the ferry terminal. So the bus ride is almost door to door (airport to ferry.)
However... if the private transport is $52 for four people, that is about the same price as the bus. So it sounds like that definitely would be the way to go. You can always have the bus as "Plan B", since it can be booked at a moment's notice (i.e. buy a ticket, hop on the bus.)