I will not be the one driving but I am trying to work out my budget for this trip and was wondering what the cost is - he has not had time to look into it and I cannot find anything online.
If he is the one doing the driving, he should be the one with his name on the contract. *God forbid you get in an accident (even a minor one), the liability issues (both "official" and unofficial direct payoffs) can be daunting and really wreck your day. Should there be injuries involved, the driver will probably find himself held in jail for several days (irregardless of fault).
That said, in my experience here, there are many rental car businesses outside of the airports. For these, with negotiation, you can usually get a decent well used "jeepeta" (small SUV) for around 1000 pesos a day.
I have a deal with one such company where I take their oldest car (usually a 4d Toyota sedan with about 200,000 kilometers on it) for 500 pesos a day (minimum 1 week). I've driven that car all over the island (North Coast to Santo Domingo, Samana, Costanza, etc, etc). And other than the occasional flat tire, I've never had a problem with it. *But I never drink and drive, and I try to avoid driving at night. (The DR is a whole different driving environment than most tourists are used to - very dangerous).*
The bus system does work well though and is very economical compared to car rentals. *
Good luck with your visit.*