Norway is a first world, hippy-green kind of country, so they should let you take your bike up on the train and cycle back.
Also, Ta Dah
(French horns) there's the
Rallarvegan, "The Roof of Norway" Kind of an Appalachian Trail for bikes.
Rallarvegen - the Navvies' road
The season usually starts in mid-July and continues to the end of September.
If you want to cycle the Rallarvegen road before mid-July, you should investigate cycling and weather conditions in advance.
The nature and terrain in the mountains is vulnerable so please show due consideration.
Take your litter with you and use the WC facilities at the refreshment and accommodation sites.
Remember other cyclists are following behind you.
Remember that you are travelling high up in the mountains where weather conditions can change in a second.
Bringing the correct clothing is vital.
In the early part of the season, you could be cycling through snowdrifts, so waterproof footwear is essential.