'Bye or leave' is a phrase I've heard all my life. I've always assumed that bye is used in the same sense as getting a bye into the next round of a competition, ie a deviation from the normal rules, while leave is used to mean permission.
I used it in something I wrote recently, and got a comment from my excellent (US) beta, that she would use the phrase 'by your leave' in that context. I had always assumed that that phrase used in that context was one of those manglings that happen when phrases are learned aurally, but the fact that she used it caused me to check a dictionary. Most of the (few) I've got access to don't have either phrase, but one had 'by your leave' used in that context.
So, what's the consensus? Is this a UK/US variation? I have found my version of the phrase online, and even in Hansard (UK House of Commons and House of Lords procedings), so it is used by people who aren't me.
Any information on the origins of either would be welcome too.