Generally, it's up to you to physically go pick up a copy of the FFL certificate from your FFL and then you mail the certificate to Bud's.
The good news is that you only have to do that once because Bud's will keep that copy of your dealer's FFL certificate on file. The next time you order a gun from Bud's, you won't have to send them another copy of that same dealer's FFL unless the renewal date of the dealer's license has expired.
Carter