When do you travel - there are often cheaper flights in the summer? Also how long do you have to get there as there is a boat that goes all along the Croatian coast. You won't be getting a train as there are none to Dubrovnik.
You have several possibilities:
1. A train to Trieste, bus to Rijeka, bus to Dubrovnik (maybe with change in Split). Long journey, 20 hours or so with waiting on stations.
2. A train to Trieste, Bus to Rijeka, ferry from Rijeka to Dubrovnik. Ferry journey takes near 24 hours. Departing Rijeka in the evening. This ferry line operates only in summer season until the end of September.
3. A train to Trieste, bus to Rijeka, bus to Zagreb (or train from Trieste via Ljubljana to Zagreb - including a short taxi trip from Trieste to Sezana), or a direct bus Trieste - Zagreb (a few weekly I think). Then you can take a Croatia Airlines plane from Zagreb to Dubrovnik. Prices on this line should be much cheaper on some days than e.g. from Venice to Dubrovnik.
What is the boat that goes along the coast?
I mentioned this boat under "2" in my post, ferry from Rijeka to Dubrovnik.
There is one more possibility.
4. Go by trains through Italy from Venice to Bari, then overnight ferry Bari - Dubrovnik.Edited: 10:47 am, September 24, 2013
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