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Hi, and welcome to JA!
The quickest way would be to fly from BUD to DBV (those are the airport codes for your cities).
There are about 2 nonstops each week during the summer -- Saturday and Tuesday -- on SkyEurope (a round trip comes to just over $200, but the prices are given in other currencies):
Malev Airlines offers 3 nonstop flights per week during the summer -- Saturday, Monday, and Wednesday. The cost is about the same as above.
Lufthansa offers daily connecting flights (through Germany), but they take much longer and cost more.
There is a train/bus option, but it looks like it might take more than 24 hours:
I hope this helps,
Malev Airlines has nonstop flights available on those exact days. The fare is about 200 USD roundtrip (plus taxes and fees of a little less than 100 USD).
SkyEurope's last flight is September 18 (though it's cheap... it only costs 40 USD including taxes and fees), but that won't help you, since it appears that Malev requires a roundtrip, so you couldn't do one leg on each airline.
Your best bet is the roundtrip on Malev, allowing you to travel nonstop on the days you want.