Caribe tours or any other large company don't go to Constanza. There are two ways - through one of the "express" services, which are few and far between but will take you straight there for less than $200. The other way is to get a guagua ($100) or a bus (Vegano - $120) to "Abanico de Constanza", which is the drop off point at the bottom of the mountain, and then another guagua ($100) up to Constanza.
This will be a very authentic Dominican experience, but the road between Abanico and Constanza is absolutely stunning, if a little hairy. No one drives it safer than the Guagua drivers though, but it will not be luxuriously comfy.
