I am sorry but I have no idea where the Terra bus depot is. I found this information at
T1 but not sure how accurate it is.
Terra Bus Service
Plaza Criolla - 27 de Febrero &
Anacoana
Santo Domingo
Telephone (809) 472-1080
You should be able to get to any bus depot in Santo Domingo Centro for no more than 200 pesos, but be sure to ask before entering the taxi. If quoted a higher rate just walk away.
Just about any hotel in Zona Colonial or Gascue will be safe. There are clean and safe hotels less than Hotel La Residence ($25 a night) but they don't have websites. Residence or LaDanae should be fine for one night. It would be wise to call them, or have a Spanish speaking person call to confirm your late night arrival.
Taxi from the airport to Santo Domingo centro will cost about $40 USD. Don't take a cab from the guys whispering in your ear "need taxi". Take the official airport taxi. The taxi accepts USD and the hotel will accept USD also. Only pesos you will need will be for bus fare, taxi, and any other purchases.
Within a block of Residence or Danae you will find a colmado for water, soda, and snacks.
Hopefully someone will read your thread and give better information on catching a bus to PAP.
This is a link to Caribe Tours as I believe they also have bus service to Haiti.
Caribe Tours C. Por A.
Best of luck on your journey to Haiti..........