Negativo on Caribe Tours, Kay
It only stops at the major stations.
To get off in the boonies, you have to take a local (mini) bus. The minimum fare should be less than 50 pesos.
Usually (always, I suppose) the local buses can be recognized by the daredevil hanging out the doorway soliciting passengers.
Probably the best place to find such a bus headed north on Duarte Highway is at a place called Kilometer Nueve. All the taxi drivers know where it is. It should cost no more to get there from the airport than to any other destination in Santo Domingo.
Later, to catch the bus back into town, stand by the road until one stops for you.
Yes, pretty good Kay.
Kilometer Nueve is a point through which all the major buses headed north on Duarte Highway pass. It serves as an informal terminal for many of them, and has refreshments, even a moneychanger I think, but not a good place to sit and wait.
The major bus lines - Caribe Tours, Metro, and Terrabus will probably not let passengers on or off there - I'm not sure, so better not take a chance. Almost all the others will, though.
When returning to La Capital, it's as good a place as any to get off, unless the local (mini) bus driver knows where you're going. The zillions of taxis waiting there are mostly legitimate - unlike those at the airport and tourist areas, they'll bargain down to a reasonable price.
BTW, this board seems to refer to guaguas as mini (local) buses, but in my experience Dominicans call any bus a guagua.