I sometimes take the train from Budapest to Munich. It takes about 6 hours, with only a minimum number of stops (Salzburg, Vienna) and the cost is around 40 Euro. I know last fall we went from Budapest to Salzburg for around 35 Euro. A great deal!
So - I would check the trains first. A second option might be a bus, but it will be a long(er) ride than the train and not as nice on many levels (no ability to walk around, no dining car, smaller space, etc.
Best of luck,
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