3-5 day cruise that ends in Bergen?

I have not been there yet, but recently posted a request for information and got some great responses on this thread: https://community.ricksteves.com/travel-forum/general-europe/trip-to-iceland-and-scandinavia-with-daughter-in-2026-lots-of-preliminary-questions

One mode of travel in Norway that was discussed was the "port-to-port" ferries that are run by Hurtigruten and Havila. They are ferry routes that evidently transport both people and goods along the coast, and you can choose the ports you want to leave from and go into. So that might be a good option for you, and the it sounds like the scenery is amazing.
https://www.hurtigruten.com/en/about-us/voyages/port-to-port
https://www.havilavoyages.com/port-to-port

https://www.vikingcruises.com/oceans/cruise-destinations/baltic/nordic-wonders/index.html?startLocation=oslo&endLocation=bergen&year=2027#noscroll

Another vote for the "ferry". We did just the 24 hour or so from Trondheim to Bergen on Hurtigruten in 2023. It's much nicer than a regular ferry. Rooms are small but as comfortable as a hotel. The food was lovely.

You could fly Copenhagan to Bodo or Trondheim.

The "ferry" can also allow you to have excursions like a larger cruise ship.

You can arrange those excursions yourself or the "ferry" company has regular ones they offer. One that they offered on the segment we took is a drive on the famous Atlantic Ocean Road. People got off the ship at one port early in the day, got on a bus, and then got back on the ship at another port.

We loved Trondheim. Especially for your 7 year old I can recommend the folk museum https://sverresborg.no/en and the history museum with lots of viking things https://www.ntnu.edu/museum

There is 1 northbound ferry and 1 southbound ferry every day traveling between Bergen and Kirkenes. Depending on the day, it will be the traditional ferries with Hurtigruten or the newer ferries with Havila.

We did the southbound coastal ferry from Kirkenes to Bergen 2 years ago. It was a 6 day trip on the Hurtigruten ship Nordlys. While the ship has a capacity of almost 600 passengers (including daytrippers without a cabin), our cruise averaged about 400 passengers.

Unlike mainstream cruise lines, there are no casinos, no shows. The views are your entertainment. Our ferry had 30 scheduled port stops. Some as short as 10 minutes, some several hours. Some in the middle of the night. A few of the night ports were skipped either due to weather conditions or there were no scheduled passengers or goods to be picked up or dropped off.

Shore excursions are offered in several ports. Sometimes the excursion would start at one port and passengers would rejoin the ship at a later port. Many of the ports can be enjoyed on your own.

Summer northbound sailings from Bergen go into the Geirangerfjord. You can fly direct to Copenhagen from Tromso, but you may need to overnight in Tromso depending on flight schedules.

Or consider flying into Kirkenes and taking the ferry to Ålesund or Bergen. You will cruise the Lofoten Islands in the daytime. Ålesund is a lovely art nouveau city at the entrance to the Geirangerfjord. You could also do a day tour to Trollstigen depending on when you're traveling. There are nonstop flights from Ålesund to Copenhagen.

In addition to the coastal views you'd get from a Hurtigruten or Havila ship, I'd want to sail into one of the highly scenic, narrow fjords like the Geirangerfjord or the Naeroyfjord. I think to see just the coast would be a shame, beautiful though it is.

I don't know whether the southbound coastal ferries make the detour into the Geirangerfjord as my northbound Hurtigruten ship did in 2022. You might have to break the journey for a day and take a separate trip into the Geirangerfjord, and perhaps do some other sightseeing in the area.
That might even be cheaper than the ferries trip into the fjord.

For the Naeroyfjord you could do some version of the Norway in a Nutshell route. One possibility would be to fly into Oslo and take the classic trip to Bergen:

• Mainline train to Myrdal.
• Flamsbana train down to Flam.
• Ferry through the Naeroyfjord to Gudvangen.
• Scenic bus ride up to Voss.
• Mainline train to Bergen.

That makes for a long day if you don't break the journey along the way, which is more difficult than one would imagine due to limited lodging options and high demand.

No the Hurtigruten does not call into the Geraingefjord southbound due part!y to having no scheduled time to do so and anyway the brief Alesund call is at around midnight.
Northbound the fjord trip never was in the schedule. It has been added as the line has transitioned from being a freight carrier who took passengers towards being a cruise business who carry a bit of freight. So you now have to choose between Alesund or the fjord.
You can't get off to explore Geiranger as it is a mere 20 minute call.

I was thinking of going port-to-port, as I did, so the OP could spend 24 hours in the Geiranger area. I spent 24 hours off the boat in Alesund, in addition to taking the detour into the Geirangerfjord, so I had time for the architecture in Alesund. I don't know what that does to the cost, in comparison to the full coastal cruise, because I never considered taking the full cruise. The point-to-point segments aren't cheap when you include the cost of a cabin, and I believe they may need to booked well ahead of time when an overnight cabin is needed..