Okay, let me see if I got this.
You are going to take a Caribe Tours bus to Santiago and then taxi to the airport?
Okay, Then you would get off at the second Caribe Bus station.
Did you know that there are publicos/"conchos" that go to the airport?
Anyway, if you call an Emi Taxi 809 581 3000 and ask for a unit to the airport, they will tell you how much...usually around RD$500. Or, knowing that, you could deal with the taxis that are right there by the Caribe Tours bus terminal...You know how much a taxi will cost so you get them to do the job for a decent price.
HB