I guess Apple has begun to literally put their money where their mouth was at last friday's press conference. As of today, they've begun to process the iPhone 4 bumper refunds for anybody that purchased one online and even for those who are still waiting to get theirs. Apparently there will also be a way to get your refund if you purchased it in an Apple Store, but we haven't received those details just yet. We'll keep you updated once we get that info.
If you haven't gotten a bumper just yet, Apple did mention they couldn't make enough for every user, so it's not a bad idea to get one quick before they begin offering equivalent options that aren't as classy..