When you get to the west coast you'll find that the B.C. Ferries system is excellent for getting around with your bike.
https://www.bcferries.com/routes-fares/discover-route-map
One trip to consider:
If you get to Vancouver Island there's the opportunity to take a day-long ferry from Port Hardy to Prince Rupert (or reverse!)....
https://www.bcferries.com/routes-fares/discover-route-map?routeRegions=NORTH_COAST
This gives you an excellent view of coastal forests, fjords, whales, etc. that you won't get by staying on the inland highway routes.
Once in Prince Rupert it's possible to get on the Alaska State Ferry system and continue that way:
https://dot.alaska.gov/amhs/route.shtml
An alternative is to head south from Vancouver and through the border into the U.S. to the first town on Interstate 5 ('I5'), Bellingham. In Bellingham you can get the Alaska State Ferry all the way (36hours!) to Alaska:
https://dot.alaska.gov/amhs/route.shtml
One thing to consider with shipping your bike: it may well be less expensive to freight to the U.S. (e.g. Seattle) than freighting into Canada, then ride across the border.
If you do get to Washington State, then you might consider going nest door to Montana and taking this highway up into Alberta, Canada (Waterton Lakes) THIS is the one highway to aim for:
https://www.nps.gov/glac/planyourvisit/gtsrinfo.htm. NOTE: closed in winter
Have fun with your planning!