Hi there, regarding your question, from my humble experience in Croatia last summer, regular ferries are only from Split to island Hvar :-(. From Split to Dubrovnik there are ferries, but i think only 1-2 times in a whole week?? and that is during season!!!. You can use maybe bus from Split to Dubrovnik or rent a car like i did. It is even cheaper combination for 2-3 passangers than bus and you can us it to visit other locations near Dubrovnik or Split . When you arrive in Split ferry port( near is main bus terminal and last station from airport shuttle) there is Nova rent a car Split, i've used their service, great assistence and really cheap rent a car. My flight was from Dubrovnik airport so i have agreed with Nova rent a car to leave car there for small extra fee (think it was 15-20€). Taxi from my apartment in Dubrovnik center to airport was 40€!!!!
Regards, Jan