The busses are actually private jitneys that hold about 12 people. While they basically run what might be called a route, there's no schedule. Route is posted on the bus windscreen. People flag them down when needed.
If you're not renting a car there will be cabs available or you can book a driver such as Mr. Brooks, a sponsor at this website. Look under the sponsor list.
There is a bus stop right outside the airport on the road (going both directions). We never took a bus to Marigot but I did see buses with the sign for Marigot in the front window.