My wife and I took the 1:45 PM a couple of weeks ago and it will have you in Barahona by 4:15PM. Great ride, very comfortable and quiet. Extremely affordable $6.00US.
Takes about 3 hours on a day where traffic is heavy and about 2.5 when its light.
From Las Americas talk to a taxi or one of the poublicos and settle on a price before heading out to Caribe Tours. I would not pay more than 15-20US. I don't know if a shuttle is available to go into Santo Domingo.