Bus Travel in Europe

Start with Eurolines.com. Also, google to find the bus lines in individual countries. I recall an Orange Bus line in Hungary, etc. Others can correct me.

Also, it would be useful if you post which countries you are going to so folks can provide more precise info.

Edit - a quick google search shows this as OrangeWays

I used Student Agency (not for student only at all) and it was great.
I did Prague to Bratislava and back. Buses were neat, had Wi-Fi had individual screens with movies.
Someone served coffee/drinks. Would do it again. Look them up!
Have a great trip.

I used Student Agency bus from Cesky Krumlov to Prague. That was a fairly short route but I would not hesitate to use them for a longer run also. It was very comfortable.

In addition the recommendations above, for options between any two points, a great place to start is Rome2Rio: http://www.rome2rio.com/. You can then check directly with the bus companies listed.

Many different bus companies operate in each country. Many have schedules online, but not in any centralized way, and not always in English. Eurolines can be a starting point for long distance buses that cooperate together. You can find bus companies for specific routes using Rome2Rio, or a Google search, or in guidebooks for each specific region. The old fashioned way, which has worked fine for me in the past, is to count on the bus service overview that my guidebook may provide (such as 4 hours, 4x/day) and then confirm schedules locally at the bus station or tourist information office. If these buses are meant for local transportation, I think they'll have less seasonal variation than (for instance) Greek buses that run much less in winter. Bus service is usually much less on Sundays.

I'm not aware of one website for all buses. Many areas in Europe are served by multiple bus lines. But my simple method is to Google my starting and ending points as in: "autobus Vienna Prague." This will nearly always get the result you need.