Bellingham - Asian Grocery
Haggen's (which for some idiotic reason everyone there pronounces it "Hagen's") has a limited selection of asian vegetables and groceries. But be prepared to pay something like $6/lb for bok choy.
Trader Joe's may have also a limited selection of certain items.
Farmer's Market might also be a good bet (again - only for certain limited items), although I haven't been in a long time. Other than that, I'm afraid the closest decent place is 1 hour away in Paldo World or Boohan in Lynnwood (as it is very difficult to get groceries across the border from Vancouver).