We did a somewhat modified Tour d’Dovre a few years ago. The stretch from Folldal to Dovre through Grimsdalen is the best part IMO. The rest of the route is OK but nothing special.

http://www.strava.com/routes/2729339302280196144

If you are in a hurry you can bypass the least desirable part of the route by taking the train to Hjerkinn and cycle to Dovre via Folldal and Grimsdalen.

From Dovre you could cycle or take the train to Vinstra and take the route called Mjølkevegen to Gol.

http://www.cyclenorway.com/routes/national-cycle-routes/overview/route-5/middelalderdalen-mjolkevegen/

From Gol you can take the train to Oslo/Bergen or you can extend your Mjølkevegen-trip by linking “Skarveheimen Rundt” or from Gol you can also the train/cycle to Haugastøl or Finse and cycle “Rallarvegen”.

http://www.cyclenorway.com/routes/national-cycle-routes/overview/route-5/middelalderdalen-mjolkevegen/
http://www.cyclenorway.com/routes/national-cycle-routes/overview/route-4/hallingdal-og-rallarvegen/

I would suggest having a few routes planned in different parts of Norway and choose depending on weather forecast.