Taxi between SDQ and Bayahibe
You can arrange any transportation you want, so that isn't a problem.
There are many taxis by the airport, most of them vans up to 6 people, so if you have lots of luggage you should be fine in those. As somebody said above, make sure you agree on the price before you get in. You can arrange the return ride with the same guy as well and you might get a better deal that way too. The cost should be between 100 - 120 USD each way, for return you might get 80 USD each way. All drivers (or most) speak English very well, so you shouldn't have problem with communication if you don't speak Spanish.
Happy travel
Denise