What is the cheapest way to travel between the cruise ship terminal in vancouver bc to seattle, washington.?

I would have to say the cheapest is the bus, plus taking the bus is a green way to go. The other idea would be to rent a car. I have done this just to get from my home to the Airport because then you don't have to pay to park it at the airport. Same goes for a port.

You can get a greyhound bus for about $30 per person. That said, you can usually rent a vehicle for a day for less than $50. It might be a better value to rent a car, because it's not much more expensive (with gas) and you can make your own stops for bathroom breaks, meals, etc.

I would go as a foot passenger on the ferry to Victoria, from there take the ferry to Port Angeles (very close to seattle) short bus ride and you are there.

Renting a car or booking a transfer through the cruise line.