In October, I plan to visit Norway where I would spend 4 days in Tromsø to catch the Northern Lights and Whales. I would also like to spend 2 nights (on the front or back end of my stay in Tromsø) in Bergen (where I'd like to do a day of fjord sight-seeing.) Does this sound like a reasonable itinerary for one person?
Sure, why not.
Weather can be an issue. Check: https://www.yr.no/en (forecast is valid max 48 hrs)
Good luck for your NL chase (may be on Fjellheisen). For the days after long nights a good wake-up coffee you will get at Kaffebønna branches.
a day of fjord sight-seeing
By rental car I recommend scenic route Hardanger. Lots of waterfalls. Hardanger bridge and a narrow fjord such as Sørfjord.
By train a day trip to Flåm is enjoyable (incl. boat ride to Gudvangen), also possible to travel through to Oslo. Search Norway in a Nutshell (NiN).
I do not recommend boat tours into Sognefjord. They last long before the scenery gets really interesting.