Looking for the fastest way to get from Dubrovnik to Hvar.......Is it possible to drive from Dubrovnik and take a ferry to the eastern side of Hvar?
You have to check the Jadrolinija ferry schedule. I took a ferry from Split which was faster/easier at the time (I was traveling a bit off season) http://www.croatiaferries.com/jadrolinija/
Well, the fastest way would probably be by private helicopter. If that's not in your budget, then the answer is probably going to depend on when you're planning to be there (the high season/low season dichotomy makes a huge difference in ferry schedules and availability). There MIGHT be a ferry you can take (or it might be a lot more complicated). Regardless, you question would be better over in the 'To The East' forum.
It is possible to drive and take a car ferry to the south-east corner of Hvar. I considered that option, but was advised against it being told the road is narrow and quite precarious in places. I instead opted to take a bus to Split and catarmaran to Hvar. The fastest way would be to time a bus to Split that allows you to catch either the 11:30 or 15:00 catamaran to Hvar. Try to buy your catamaran tickets in Dubrovnik or possibly online at www.jadrolinija.hr. Your options are more limited outlide of high season (June-Sept).