Revealing mistake: In the scene where Pai Mei shows Beatrix the short punch through the timber, the hole he punched through it is not solid wood but a fake veneer, MUCH thinner than the timber that is shown. (00:53:40)
Revealing mistake: When they show a close up of Pai Mei's face, look at his eyebrows. You can see the actor's real brown eyebrows underneath the fake white ones.
Chosen answer: The way she talks to Budd as he lies dying, seems to indicate that she has disliked and hated him for years, plus the fact that she feels that he was not "worthy" of killing Kiddo (seeing how Kiddo was a fantastic warrior, while Budd is an alcoholic hick). However, it would be difficult for her to get close enough to kill him earlier, as he would not buy any excuse why she just came visiting. But when Budd actually invites her over, she gets a chance to get back at him, and in the same while take the credit for killing the Bride and retrieving her Hanzo sword for Bill. Vengeance and personal gain in one swoop.
Twotall