I don't know the route you're planning through B.C. but when if you're going through Vancouver, there are a few roads to watch out for. Bikes are not allowed in the Massey Tunnel on Highway 99. There are shuttle services if you need them, but I'd suggest modifying your route in this area. The Trans-Canada Highway from around Abbotsford west is rather hectic. If at all possible, try to use another route.

If you want a slightly different experience, you can take a ferry from Prince Rupert to Port Hardy on Vancouver Island and then cycle south to Victoria. This way, you can bypass Vancouver. From Victoria, there are ferries to get you into Washington State. On the Island Highway, the terrain is mostly rolling and moderate, but there is one big hill at Malahat Pass. This is between Duncan and Victoria. You can bypass this by taking the ferry from Mill Bay to Brentwood Bay.

There's a lot of good information on touring B.C., Alaska and the Yukon at http://broughton.ca/bcakfaq.html