Are there any reasonable alternatives to the 13 hour train ride to get from Bucharest to Budapest?
I searched for budget airlines that fly that route, but I didn't find any. If you take the train, the direct night train probably would be your best choice.
You could fly from Bucharest to Cluj with Tarom (http://tarom.ro/; costs $55 if you book in advance), then fly from Cluj to Budapest with WizzAir (http://wizzair.com/; costs $10 - $30 if you book in advance).