Anne, it was quite a few years back (like maybe 15) but at that time, it was just a matter of applying (by mail and telephone) as a non-resident account. I don't know what the rules are now but at that time, as long as they had our signatures on their cards, which we did by mail, they were quite happy. I just added on-line banking about 4 months ago when they gave me a generic, non-resident SSN for logging in, also by telephone. Most US banks have 800 numbers that work from Canada - just Google the bank of your choice for their website. That Bank of America is www dot bankofamerica dot com and that site should give you the 800 number to get started.
As an aside, we have to fill out a form every couple of years to state that we are not carrying on a business in the US. Bear in mind that we are NOT doing business IN the US - we are doing business WITH the US - I'm sure Malcolm will confirm that there is a big difference.
Good luck -- it's worth the effort!!
Glenda
Glenda