What is the easiest was to get from Dubrovnik to Split and back in early May?
I found the bus service between Dubrovnik and Split to be very efficient and reasonably priced. You might ask your hotel or sobe to call the bus station and reserve a ticket for you. You pick it up and pay for it when you arrive to catch the bus.
I guess you could rent a car, but public transport is very efficient, I'd say either by bus or by ferry. Bus is faster (3.5 hours?), but the coast is very curvy. I don't get car sick, and I was wishing for gravol-and I only went as far up the coast as Bosnia-Herzegovina-I also think the bus is a bit cheaper, bit neither were very expensive. Ferry is slow (about 8-9 hours), but I enjoyed the coastal route that it took-it stops in Korcula and Hvar to drop off and pick up passengers. It only runs a couple days a week though. Both the bus and ferry ports are basically side by side in both towns (note that in Dubrovnik you'll have to take a city bus to get from the old town to the port), so that isn't an issue. Also, you probably only need to buy bus tickets a day or so in advance; there are multiple trips between Split and Dubrovnik daily. I find the bus sites more difficult to navigate to find timetabling information than the ferry sites (but your hostel/sobe/hotel should be able to provide more info). You can easily purchase ferry tickets online through the Jadrolinija website, which is very user friendly.
I would recommend flying via Croatia Air. The tickets will be about $50 a person. Of course if you want to see the amazing coastline flying isn't recommended.