Actually -
You can't bike most of it even if you wanted to.
There ain't no road. There definitely isn't a road between the northern tip of Vancouver Island and Prince Rupert - then it's island hopping from there north.
Here's a possibility -
Take the ferry from Vancouver to Nanaimo - then bike north on Vancouver Island to the northern tip at Port Hardy. That way you slowly get out of civilization and can acclimate to fewer and fewer services. North of Campbell River there ain't much. It's about 300 miles.
Then take the BC ferry from Port Hardy to Prince Rupert. At Prince Rupert you can do one of three things
1) Take the Stuart Cassiar Highway north to Watson Lake and then head to Skagway ending in Juneau.
2) Take the Alaska Marine Highway north - possibly riding Prince of Wales Island - but definitely doing the loop from Haines to Kluane to Whitehorse to Skagway.
3) Take the BC ferry out to the Queen Charlotte Islands and ride out there before continuing on with #2
It's 150 remote miles to the Cassiar Highway Junction - then 450 even more remote miles to Watson Lake - then another 300 miles to Skagway. The Haines-Kluane-Skagway loop is also remote, but not quite as remote as the Cassiar. The loop is about 375 miles. You would need a minimum of two weeks plus to do Vancouver Island and the loop and the ferries - three weeks if you added some exploration of the Queen Charlottes or some combination of Ketchikan, Wrangell, Petersburg, or Sitka in southeast Alaska.
It sounds like you do not know the area well nor have you much experience with such cycling. I would STRONGLY suggest northbound on Vancouver Island and the Yukon loop with, perhaps, some small rides at intervening ferry stops.
Check out BC ferries -
http://www.bcferries.com/schedules/inside/
Remember that the Port Hardy to Prince Rupert ferry runs every other day.
Alaska Marine Highway -
http://www.dot.state.ak.us/amhs/Plan...7/SEbw_S07.pdf
AMH ferries run 4 days a week out of Prince Rupert with stops along the way.
Glad to answer any question you have.