woohoo, someone said I had a good theory!
I think Elle killed Bud because when it came down to it, Elle was the one who wanted to off the Bride. She's the "new" girlfriend jealous over the ex. She was always jealous of the Bride because The Bride and Bill shared something Elle and Bill would never have. The Bride was meant to be her kill (hence the hospital scene in vol1) and since Bud got the job done before her, she killed him out of spite. She then called Bill and claimed that she was the one who finished the Bride off, marking her superiority over The Bride.