British Columbia is huge. It contains elements of the Plateau, High Plains, Coastal Areas, and Islands. To narrow down one type of archery tackle would be a very broad generalization. Yes, sinewed bows were used but other bow types were used as well. Everything from simple self D-bows to the elaborately painted sinew-backed paddle bows can be found there.
Canada, in my opinion, has a much better understanding of their First Nations cultures than we do. I would try to hit as many local museums as possible and see what they have on display.
Having said that, a safe bet would be to use a softwood for the bow and hardwood shoots for the arrows. Yew or juniper for the bow, for example, and osier for the arrow shafts. Sinew backing is also a safe bet, as already mentioned. A simple quiver, for holding the bow and arrows at the same time, made of a case-skinned small deer or large otter skin would be fine. Most arrows I've seen from that area were foreshafted with very small arrowheads. The fletchings would be from sea birds or birds of prey... but you can't use those so goose feathers are a good substitute. Bowstrings and bow backings were usually made from very long sinews, like bison backstrap, as opposed to leg sinew.
It's hard to read the text on the picture below, so here's the link:
http://www.bcarchives.gov.bc.ca/exhibits/timemach/galler07/images/abbcmapm.jpg
