Looking at the times for this coming Monday, the only direct bus is the one at 1600 (arriving at 2015).
The next three connecting services, departing at 0555, 0635 and 0935, are all too early for your needs. The next service isn't until 1400, which gets you to Budapest (N�pliget) at 1550. You've then got a 40 minute wait until the 1630 service to Kaposv�r, which gets you there at 1930.
There's an alternative (slightly quicker) route available at roughly the same time: The 1410 bus will take you to Sz�kesfeh�rv�r bus station, arriving at 1550. There's then a 45 minute wait for the 1635 service to Kaposv�r which gets you there at 1925.
http://www.menetrendek.hu/cgi-bin/menetrend/ht ml.cgi
Although some of the train journeys do involve multiple changes, it's possible to do it with a single change. For example (based upon times for this coming Monday), you could take the 1031 train from Győr to Budapest-Kelenf�ld. It arrives at 1202. The 1252 service from Budapest-Kelenf�ld to Kaposv�r gets you there at 1624.
However, you can do it quicker (and with more frequent services) if you're prepared to make 2 changes:
http://www.mav.hu/english/index.php
Chris