Yeah, 001 is BMO. It is said that BMO was the first bank in Canada, so I guess that's where 001 came from. And BMO names many of their services with "First Bank". Seems that they are proud of it.
One thing needs to be indicated here: the 3 digits codes discussed above are definitely NOT "Swift Code" of banks. They are the "Institute Code" or "Bank No.". "Swift Code" is a much longer one consisting of letters and digits. Please contact your bank for exact info.