This should help you: http://www.mavcsoport.hu/en/node/9235
The fastest train if it were going through would be 7;15 hours. With issues at the border, who knows. I have a sort of dark opinion because i had to help a couple of guests about a month ago when they tried to get from Austria to Budapest. Then we had another guest that ended up in a refuge camp by accident, a couple showed up 4+ hours late, etc...... The whole Budapest - Vienna issue has been well resolved so that's no longer a problem, but then again it never was a problem until the day that it was a problem and no one could predict that day. In my recent travel through Croatia, Montenegro, Serbia and Hungary I never saw a migrant. But then i when heading south i drove and when heading north i flew. Plenty of low cost carriers; for instance Montenegro to Serbia was about $70 and Serbia to Hungary about the same.
I checked on the ticket BUD to MUC. The 15th is a problem but if you leave a day earlier (don't Budapest is too good) or if you leave a day later (perfect) a Round Trip ticket can be had for about $150 or a one way ticket for about $270. I am certain someone here can explain that to you. It's a 7:15 hour +++ uncertain train trip or a 1:15 flight. So, 8.5 hours or more door to door by train or 4.0 hours door to door by plane.