I suggest you rent a car. It will give you much more freedom. You can pick up the car at Las Americas Airport (SDQ) and then it is a short drive to Juan Dolio (will cost you to get there by taxi half of what the rental for the day will. Then you can drive around to see all the sites, making day trips. When you are in Bayahibe, you will be two hours from Punta Cana and Boca de Yuma, half an hour from La Romana and Casa de Campo. Bayahibe is about an hour East of Juan Dolio.
Otherwise, you can do it by public transportation. Is cheap. Just ask the locals where they take their buses. They are safe (take normal precautions), although you will spend lots of time waiting and they can get crowded.
See
http://www.dr1.com/national for a recommended car rental.