All the ferries for Croatia from central italy depart from Ancona.
Rome - Ancona is a 3 or 4 hours drive, depending if you go thorugh L'Aquila or Perugia.
Either way considering a two days trip (+ the ferry) in central Italy between Rome and Ancona, with food and wine and amazing landscapes is a good idea, having the time.
If you don't have the time, go for the plane. about 4 years ago
I know this is kind of late but this might be useful for someone else:
I took a ferry from Bari (which is central Italy) to Dubrovnik and back a couple of months ago. It was not cheap but it was 100% worth it, inbound was an overnight trip, starting at about 10pm and arriving at 8am, which was lovely. The food was delicious, and I had a comfy bed in a shared bedroom with another woman, with private bathroom, just like a hotel room. The way back was faster, starting around noon and arriving in Bari around 7pm, so I didn't get a room that time (though you can if you want, I just thought it was pointless).
It does take a lot of time, and just like planes, you need to check-in and go through security and all. Still a great experience, definitely worth doing at least once, so I'd say that's "better" than a plane.. over 3 years ago