Hello Linda,
Citybird only flies to Punta Cana and Puerto Plata. Maybe next season they gonna fly again to Santo Domingo (I hope so!). So if you really want to fly with them, the only way is fly to Punta Cana and then take a transfert to Bayahibe. You can check Neckermann, Sunsnacks or Pegase (last one more expensive). The transfert from Punta Cana to Bayahibe would take approx. 2h30.
Now you can also fly with Sobelair who still flies to Santo Domingo (much closer). For the touroperators, I think Belgian International (?) works with them.
Do not hesitate to email me for more information.
Good luck,
V?ro