anyone notice that the Yakuza lord that kills Oren Ishii's parents is wearing the same rings as Bill???
ALtho' I still think the Bud intro was perfect, I do agree that Elle's characterisation may be ALITTLE off.
not so much inconsistent as it was ... ill-realized direction wise.
Example:
In the first one, we see Elle giving The Bride "a gift" ... the gift of a death whilst in a coma... "a luxury few in our field are given"... paraphrased... she even said, "just because i hate you, doesn't mean that I don't respect you..."
So, ok. She respects Beatrice enough to grant her a painless death... and she respects her SO MUCH as a warrior that a lower person (in her eyes...er EYE

)doesn't ahve th eright to do her in and must be punished for doing so (which is a common villainous trait -- this is nothing new in comic books, villainy movies, and kung fu movies).
HOWEVER, we are NOT given alot of information regarding Elle and Bud's dynamic. So in that, you are correct.
With regard to Elle and Bud, instead of working a+b=c, which is ideal, we have to go c-a=b.
meaning, instead of showing th ebad dynamic between Elle and Bud.. and then Bud killing Beatrice, whom Elle respects, so therefor she must kill Bud.... we have to go backwards, sorta.
Because she respects Beatrice so much and Elle was willing to risk incurrin gthe wrath of Bill, she MUST have really hated Bud. She was rather snippy with Bud the whole time.
Plus, she was obviously a woman who over-stepped her bounds.
She contradicted Pei Mei ... and got an eye out b-c of it
She tried to execute a plan that was not Bill's directive
She killed Bill's brother and was gonna frame Beatrice and take credit for her death....
this was a woman who probably simply thought she had it in the bag.
But of all the character dynamics, you're right: this was the weakest, if you do only deductive reasoning.