nuremberg to pilzen

The best seems the bus which leaves Nuremberg at 6:50 and arrives to Pilsen (Plzen) at 9:45. The bus goes all the way to Kiev. All other connections - you have to change at least once. You can find the connections on Deutsche Bahn website or here:
http://www.idos.cz .

Train works to with a Bayern-Boehmen Ticket.

All in one day or will you spend overnight in Pilzen? The Bayern-Böhmen-Ticket is an all day pass for one day for all the regional trains in Bavaria plus in the western part of Czechia as far as Pilzen. 28€ for one, 6,60€ each added person up to 5 total. Trains run from Nürnberg to Schwandorf where they connect with a train from Munich to Pilzen (and eventually to Prague). Or you can use any other combination of regional trains from Nürnberg to Pilzen.

There are not many busses between Nürnberg an Plzen and most of them run at inconvenient times. Personally, I'd take the train via Cheb ( normally same platform transfer with the Czech train waiting for the train incoming from Bavaria) since landscapewise it's much nicer than the rather dull route via Schwandorf. +) And you could take an intermediate stop either in the pretty town of Cheb or in the Belle Epoque spa of Marianske Lazne. I'd travel on a Bayern ticket as far as Cheb and then book single tickets for the Czech leg in the E-Shop of the CD. So you can choose your train at will, while the Bayern-Boehmen ticket restricts you on trains of the category EX and lower.

+) Please note that the line Schwandorf-Furth im Wald-Plzen will be closed for construction several times this summer.

I thought I read that if you were using a db train pass, you could arrive in Nuremberg and at no additonal cost continue to Pilzen

we took Flixbus from Nuremberg to Pilzen. It was comfortable and quicker than the train. The only issue you might run into is since the bus is subject to traffic, it can be delayed.

The German Rail Pass includes the IC bus from Nuremberg to Prague, but it does not stop in Plzen.

we took Flixbus from Nuremberg to Pilzen. It was comfortable and quicker than the train.

That seems to have changed. The fastest train connection is 3:07 while the fastest Flixbus connection, checked for three random dates in May and June, is 4:50 with a transfer in Regensburg in the middle of the night (for an overview of all carriers look up www.busliniensuche.de). It's only on the nonstop connection from Nuremberg to Prague where the bus beats the train.