All of my travels to Constanza have been by private vehicle and for that reason it is difficult to pull the loose ends in to get some concrete information for you on public transport
The distance from S.D. to Constanza is about 135 km, 2.5 - 3 hrs travel time. You are most likely going to have to change buses at Bonao. I do think Ken has it right with Caribe Tours as far as getting to Bonao. Bonao is the town having the nearest access to the primary mountain road to Constanza from the Autopista Duarte. I would recommend when you get on the bus from Santo Domingo to Bonao ask the driver and/or the other passengers where to drop you off, the nearest parada (bus stop) in Bonao for the guaguas going to Constanza. Best to start of early am, that way you increase your chances make a prompt interchange at Bonao without having overnight there. If you have the courage and really want to enjoy the vista of the ride, sit on the right side of the guagua. The guaguas do not operate at night for very obvious reasons.
If you have not made any accomodation arrangements for Constanza, I have a few suggestions. Regards, PJT