I travelled from Bergen to Nordkapp in June 2005 and, although the higher level roads were clear, there was still plenty of snow and frozen lakes by the roadside when you were in the mountains around Geiranger Fjord, etc. Even in June the temperatures were decidely cool at times especially when raining; weather was a bit like a Scottish spring. I found I needed my balaclava & merino wool baselayers quite a few days, although towards the end of the holiday (early July) it did start to get quite warm e.g. low 70's
I think you would be taking a big risk with the weather even thinking of riding that far north on a bike in March or even April. Having lived in the far north of Scotland, which is a considerably lower latitude than even Bergen, I would think you would be lucky to have 6 hours light per day in Feb. You would almost certainly encounter snow & find some of the more intersesting roads blocked / closed (e.g the Trollistigen pass, or roads into & out of Geiranger Fjord).
The short daylight hours would mean you would also miss the changing scenery which, for me, was one of the highlights of the trip. There are also a lot of reindeer wandering loose above the Arctic Circle who had a nasty habit of being on the road or crossing the road as you approached. I probably had to stop dead at least a dozen times. I would certainly not wish to ride after dark with so many bambi running loose; all the HGV's have bull bars for this reason. Northern Norway is also pretty sparsely populated & the roads quiet e.g. there may not be much help available if were to come a cropper in the dark.
I stayed on campsites & in campsite hytters during June as hotels were all very expensive, and hotels were none too frequent in the more northern areas. I suspect you may find campsites and accomodation thin on the ground in March / April as this is well before the tourist season (even in France, Spain,& the UK many tourist places do not open much before Easter). In the northern areas June - mid Sept seemed to be the tourist season.
I love Norway and would intend returning however this would be another summer trip. There is something magical about 24 hour summer daylight in northern latitudes.