There are multiple good ways. Cascade Bicycle Club does it (in reverse) every year:

http://shop.cascade.org/content/events/rsvp-details

I think their 2nd day route (Bellingham to Vancouver) is a bit too long and convoluted, probably because they head way east to avoid overwhelming the border crossings near I-5 and the western, more heavily-used Fraser River crossings. But their route from Seattle to Bellingham is solid.

Between Bellingham and Vancouver, I'd just buy a Vancouver area bike route map and make it up as you go along (note: Vancouver area bike route maps cost money and are what you want; Vancouver city bike maps are free and don't get you to the border). Avoid heading south into Richmond, but any Fraser River crossing east of that is fine, and the route to the border should be easy to pick out from there). Use the Whatcom County bike map to get to Bellingham (https://www.whatcomsmarttrips.org/pdf/CountyBikeMap.pdf) then take the RSVP route from there.

The ferry to Victoria/Olympic Peninsula route is more scenic, but much longer. I'd avoid it in favor of the land route, which is plenty scenic, particularly on Chuckanut Drive. If you were riding south from Seattle, I might advise the ferry route, as it's hard to avoid I-5 otherwise, but between Vancouver and Seattle it's easy to stay off I-5 and still see some nice backroads.

Incidentally, riding Interstate highways in Washington State *is* legal, outside large metropolitan areas (and even legal then if there is no viable alternative route, like near Ft. Lewis). So you could take I-5 much of the way (I don't know if Bellingham or Everett count as metropolitan areas). Just FYI; don't do this, as the backroads are much nicer.