The train duration depends on which route you choose, where it connects, and if the specific train you’re on is an express train (faster, fewer stops) or regional train (more stops). With a rail pass, you can hop on and hop off at will during each valid pass day.

Bahn.de will help you find most train routes and durations in Europe. Checking Berlin Hbf to Bergen (N), fastest duration is 25 hours, 40 minutes with 4 changes — Hamburg, Copenhagen, Gothenburg, and Oslo. That would require (I think) 2 pass days, which is good, because you should break this trip up, anyway. Copenhagen and Hamburg are worth at least 2 days/1 night, in my opinion, and Oslo and Goteborg at full day each. I wouldn’t normally recommend these as standalone destinations—except Copenhagen—but since the train you’ll be on goes right to each central station, anyway, they’re worth a stop.

From Bergen to Amsterdam, I recommend coming the “other” way — ferry to Stavanger, train to Kristiansand, car ferry to Hirtshals, train to Hamburg, train to Ams C. Bahn.de shows this one 32 hours with 7-8 changes; it backtracks you from Bergen to Oslo, Got, Cph, Ham, then Amsterdam. I’d prefer to come down from Hirtshals, the way I suggested. Your rail pass might still give 30% discount on that ferry, but it’s not too expensive regardless. I’ve done that NO/DK crossing many times.

Berlin to Bergen is 25 to 32 hours — not my idea of a train ride. Bergen to Amsterdam is 32 to 35 hours. Here’s the link to the bahn.de site Don mentions. Use it for train schedules anywhere in Europe http://reiseauskunft…

I’d look for cheap flights although Scandinavia and cheap are seldom seen in the same sentence.

Is there a specific reason for wanting to visit Bergen? Spending a lot of time in Norway, or elsewhere in Scandinavia, might be tough on your budget since you aren’t off-setting it with any place that’s really cheap.