I researched this a bit a while back but decided against it. It's a long way and a lot of hassle. This guy have a lot of info on his website and also offers private taxi - all the way or just taxi for travelling to bus stations etc., have a look:
I also found an option to hire a car in Punta Cana airport and drop it off at Puerto Plata airport, this company Sixt/com had a good offer, but still it was not worth it for me, so I flew to POP at the end.