To go from Dubrovnik to Venice you have several options on disposal.
Dubrovnik - Bari by boat and then by train to Venice
Dubrovnik - Trieste by bus, and then Trieste - Venice by bus
Dubrovnik - Split by bus or by ship, and then Split - Venice by ship (not sure when they start ship line between Split and Venice)
You can rent a car, it is approximately 12-13 hours of driving or you can hire somebody to take you there
Answer to your questions would be: the cheapest way bus or boat; the fastest way rent a car or to hire someone to take you there
Have a nice stay in Dubrovnik and Croatia