travel from Budapest to Dubrovnik

I would say fly. Check out Croatian Air first. The train service in Croatia is either non-existent or not efficient. We went from Bled, Slovenia to Dubrovnik, and the only logical option was to fly out of Zagreb. Going off of Rick's driving time map, it would have taken us 11 hours to drive from Bled to Dubrovnik... We fly one way out of Zagreb for $60/each. So you may be able to find a decent deal since you're going out of a major city.