Obviously some variation but I can give 2 prices. A driver from the capital in a modern people carrier costs RD2,750$ per day not including gas. Buying him meals is optional, pottering around the city probably not required, a full days drive is probably a nice thought.
A driver in the Bavaro area is RD4,000$ per day on the same basis.
These are prices that were offered on full weeks employment, not only a single days driving, nice cars, nicely dressed drivers that speak enough English to get you where you need to be.
This is a complete day, from 2 hours to 18 hours, no difference, if they can not book the car out as you may need it, then you pay!
Or you can hire a banger with driver each morning from anything from RD1,500$, but expect break downs and a bit of haggling (hassle). We used to go to Boca on a pi$$ up now and then, all day and would pay a local taxi RD1000$ to take us and take up home, he would also be drunk on the return journey.