Idefix: This is Asterix under a different name!
I am not sure that there are buses that go there. I know there are not right now from Santo Domingo, at least that are easily available to newbies (or Gauls).
You best bet would be to deal with the Taxi drivers (pirates but pretty good guys) and make a deal for a straight drive there from the airport.
Now it is possible that one of the Romans on this board might have much better information and even guide you on how to :
1) get from Santo Domingo Airport to Santo Domingo city
2) where to find public transportation to Las Galeras (Samana)
3) maybe give you an idea of how many sestercios it will cost you.
I know one way, but that requires you to spend a night in Santiago...if they don't come up with something better, I can fill you in. there is time...
That's my bone for Idefix....
HB (Asterix)