I haven't dealt with Bud's but have with The Gunsource online, they'll want a copy of your FFL's license sent to them, after payment and FFL copy is received, they'll ship it to your FFL. They may already have a copy if they've shipped to your FFL in the past, TGS had one on file already for mine, so they shipped it the next day.
I just bought an Optima Elite from Whittakers, they do the same thing, but they'll accept the FFL copy by fax, called my FFL and they faxed the copy, this one was ordered over the phone.
Tim