The Bus line that runs from near Parque Enriquillo uses guaguas, and they are often crowded. In the past, I was charged an extra fare for my bag coming from the SDQ airport. That made it 160 pesos rather than 80. I imagine that this was illegal, but I am not so poor that I am going to fight over a lousy buch and a half.
Other times the Juan Dolio bus took me and several other passengers inside the airport right up to the door. It can be a bit crowded, but it is not a long trip.
There are larger buses that might drop you off at Juan Dolio headed for Sam Pedro Macoris.
They will fill the bus as full as they can. If the bus looks too full to suit you, take the next one. They seem to leave every 20 minutes or so.
They start dropping people off on the other side of the Rio Ozama Bridge. They also pick people up.