Canadian business working with Amazon.com
In order for a U.S. bank to open a business account for you in the U.S. you need to have a business registered in the U.S.
One option is to open a company in the U.S. (such as an LLC) in a state with minimum formalities and cost (such as Delaware, Wyoming or New Mexico). You would then travel to the U.S. with the company documents and open a bank account (read more about opening a bank account in the U.S.)
Another option is to register your Canadian company as a foreign entity in the U.S. You would still need to pick a state where you would register the company, and usually this process is a bit more complicated, as your Canadian company documents would need to be certified in the U.S. embassy, since Canada is not a signatory of Apostlle Convention.
With that being said, it is possible that a bank would accept EIN letter as the only document, or even accept your Canadian documents without certification, but I wouldn't count on it (check with the bank though).
We can help you with both courses of action, however you need to decide on which one you want to go with.