This guy wrote pretty much the definitive version of getting from Seattle to Vancouver by public transit. The write-up is almost 2 years old so you'd be advised to check the relevant transit agencies for route and schedule updates. But the part about walking across the border should still be the same:

http://seattletransitblog.com/2009/0...ublic-transit/

And here's a link for the opposite direction, though it's from 6 years ago:

http://www.travelblog.org/North-Amer...log-27250.html