If you have time for whole day tour it will be worth the Bergen Card. Princess cruise ship just stayed half day and had to embark no later than 1:30 PM. Bergen Card has a lot of restrictions, compare Copenhagen Card we used in 2102 Bergen card needs a lot of improvement.
As someone who tends to cram a fair amount in to a day in a city, the Bergen card was definitely value for money for me. There's enough variation in what it covers to have a dry or rainy day alternatives - but still bring an umbrella.
We got 3 day Bergen cards- they pay for themselves if you plan properly- all museums and art galleries are free- reductions in the Ice Bar, on the hop on off buses, we got a substantial discount on our fjord cruise, 50 discount on the cable car though the queues can be awful, free travels on all ordinary buses and also the light railway which takes you out to a shopping mall. We also for 10 off food at TGIs which is quite significant!. Get them at the tourist information which is open all day every day- excellent service.