I can't give you ridning times on a bike, as we did it with a Land Rover and thus could drive further per day without getting a sore butt! We used 10 days for Oslo-Northcape-Oslo (north via sweden).
I can tell you that the main roads are pretty much all good tarmac, and speed limits are usually 80 km/h.
The train doesn't go farther north than Bodø, and to take the train to/from Bergan, you have to go via Oslo... Look at www.nsb.no
for train info.
I'd say the best part of the trip up north was Lofoten. I would drive extra hard to "save up" a few days exploring the lofoten islands. Have a look at our website: www.dunia.no
under the Norway part of our "diary".
We unfortunatly didn't go on the "Atlanter havs veien" (Atlantic sea road) from Bodø to Trondheim, because of too little time, and me being sick as a dog, but this is supposed to be one of the most beautiful roads in Norway.
How enjoyable it is up north depends of course on the weather. The weather can be great and it can then change to crap in 5 minutes...
June is good in terms of the midnightsun. In fact, You might find yourself doing things and then suddenly noticing that it's 0300 in the morning while you thought it was maybe about 2200 in the evening!