I'll be traveling through Greece, mainly island hopping coming from Turkey, for the first time in late May and my goal is to get to Croatia (specifically Dubrovnik), but I'm not sure of the best way this could be done... If I'd have to rely on a patchwork of buses or what. Any insight is very much appreciated. Thanks!
Using the wonderful website Rome2Rio and picking Athens as the Greek starting point, here's what I got: http://www.rome2rio.com/s/Athens/Dubrovnik. It shows that the bus ride is almost 22 hours and involves 3 separate buses, including one that only goes 3 times a week. So I'd definitely fly; use http://www.skyscanner.com to find flight options. Remember that if a one-way ticket is too expensive, you can book a round-trip ticket and just not use the return portion.
If you're coming from a Greek island rather than the mainland, you'll almost definitely have to fly unless you even more time for the ferry to the mainland to pick up your bus(es).
I also recommend flying. I would only choose bus if you have a week to stop and actually see the other countries along the route. Greece does not currently have any international train service, and neither does Albania, and Dubrovnik is also not on a train line. You can't rent a car in Greece to take to those countries.