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http://www.eurolines.lv/

Eurolines is one company that does the route. Their website can be viewed in English you can buy tickets online.

I'd get a bus. Buses are actually quicker than rail in Russia. Also there are lots of buses that do the Riga - PBer route, so you will manage to find one. Most people don't book tickets in advance...

Well, maybe there isn't a direct one, sometimes you have to go out of your way a little, take multiple trains/buses, etc. I remember once when I took the train from from Warsaw to Vinnitsa, Ukraine I...