some directions...
From Bayahibe take a taxi to Transporte Asomiro bus station in La Romana, 500 pesos. Just asked the last taxi driver I used there.
Ticket from La Romana to Santo Domingo, 105 pesos p/p, departs every 30 minutes. Ask them to leave you in Plaza Lama in Av. Duarte where there are plenty of taxis you can use.
Taxi from Plaza Lama to wherever you go will be from 100 to 200 pesos.
In the way back, ask the taxi to leave you in Parque Enriquillo, tell him you are going in Transporte Asomiro to La Romana and do not get out of the taxi until you are sure he found it (Parque Enriquillo is a very messy and not so nice place to be alone in).
Total is around 1600 pesos (about 50 dollars for one person). Now, I hope you speak some spanish or have your interpreter with you all the time.
Jess