Dubrovnik to Split in mid May

Is there a reason you want to take the bus because there is a ferry from Dubrovnik to Split. Check out
Croatiaferries.com. On the left click on ferries to/from mainland then scroll down to Dubrovnik to Split click on and the days and times will be there for each month. A much nicer mode of transportation.

First off, there is no train, perhaps you know this already.

As for bus, Flixbus is just fine. If you are flexible on time, then you can most
likely pick a departure close to your date, but you will pay more, and there
can be inconvenient departure times. I'd book once I knew what day I need
to travel.

It's worth noting that the time required either way is about the same; in fact
the bus may be a bit faster.

The bus and ferry terminals in both cities are pretty colocated.

My wife doesn't do well on the water. Thank you both for the suggestions.

My sister-in-law always gets seasick. While on the ferries from Dubrovnik to Korčula and then to Split she used those wrists bands recommended by many and sat outside on the top tier. It isn’t too long a ride and she was fine. Her daughter was with us and she suffers from motion sickness, hence the bus would have been worse. She also wore her bands.

As to "not doing well on water", this is a catamaran, and is very smooth and not bouncy. Great coast views. We've taken Flixbus as well, and I have not had a bad trip with them - inexpensive, newish buses, stop every 2.5/hr for driver smoke break.