Leaving the SDQ airport to get to the city (Parque Enriquillo, across the bridge, or points along this route), you go up to the top floor of the SD Airport and there will likely be a cabbie in a yellow shirt who will take you to the guagua dropoff point on the highway. The odds that there will be a guagua waiting are quite good. I have never had to wait. Guaguas from San Pedro and beyond tend to transfer their passengers here if they are mostly empty. If one is too full to suit you, wait for another. I have never had to wait,and the guagua has never been crowded.
Guaguas that will drop you off at the entrance to the SDQ Airport you can take at the Boca Chica guagua station.They are not supposed to, but the might charge you double (70 pesos) to drop you off at the stop. Assuming this is during daylight hours, you will find motoconchos and taxis there that should not charge more than $200 pesos to the terminal, perhaps $300 pesos for a cab from the highway to the airport. It sort of depends on how much luggage you have. You will see cabs dropping off people at the guagua stop across the street if none appears. The fare from Boca Chica to the SDQ entrance was $35 pesos last September.
I would not try this at night. Perhaps after dark you could take a cab to Boca Chica and take a guagua from there into SD. I am not sure how long that you might have to wait. The airport is a safe place to wait until dawn, I think.
Of course, you can take a cab into SD at any time, but you will need to haggle, and it will cost several times as much. This would be easier inside the airport, you might not want to haggle with someone who has already grabbed your bag.