Here are some threads that might help you
http://www.dr1.com/forums/showthread.php?t=30510&highlight=buses+Punta+cana
Also found this:
There are a few really detailed posts including the schedule, prices etc. In the last while , you'll find them.
Alsays search first then ask, a lot fo the time it's here for you already.
Here's a hint of what's in store:
There is an Express Bus to Santo Domingo from the Bavaro bus stop that leaves at 4 pm. If your flight gets in at 2 pm, you could make this bus, would be kind of risky if your flight gets in at 3 pm. These buses leave on time. The next bus is at 7 in the morning. It takes almost four hours to get to Santo Domingo. The cost is less than US$10 (about RD$120, price could have changed recently.)
If you miss that bus, catch a bus to Higuey (about RD$25). These buses leave about every 15 minutes. From Higuey, buses leave on the hour for Santo Domingo, with the last bus at 6:30 pm, so you have time to make this bus. The cost to Santo Domingo from Higuey is less than RD$100. Just check what the going fare is. It is a standard fare. You should cash money into pesos to pay for the fare. The bus will probably drop you off in Enriquillo Park -- in the midst of the Avenida Duarte bargain price shopping district. From there you can take a RD$60 taxi to your destination in Santo Domingo, or just catch any of the cheaper transportation ways any fellow passenger will recommend.
ricktoronto
And, like he says, there are more in the Search Function.
HB