This is a really tough question to answer as the whole coast is beautiful and any part you skip you may want to come back to cycle another time.

How many kilometers do you plan to ride in a day on average?

I think what you suggest is a good starting point. Bergen to Askvoll and then take the route you have made to Ålesund (it’s amazing as you know). The coastal route is also beautiful but come back and do that another time! You could skip Kristiansund – Trondheim with the express boat (it is a nice quiet area of the country but once again you can come back and do it another time).

Once you are in Trondheim I would try and do it all as Sandnessjøen-Bodø is the best part. You could take the Hurtigruten (deck ticket – around 90 euros) and skip the first part to Brønnøysund. (Trondheim – Brønnøysund)

https://global.hurtigruten.com/port-to-port/?_gl=1*xxen0y*_ga*MTI4NjIwODIyMy4xNjg0OTE5MTAw*_gid*MjAyNjE4NzU2LjE2ODUxOTE0MjQ.#/

Bodø to Tromsø you should be able to do it in a week or so.

I think three weeks is enough with these options.