Wonder Woman recently became a demi-god. Bugs Bunny is a comic god and it's unfair to have him in this tournament.
This gets a lot more interesting knowing that these two once shared the same universe. Superman & Bugs Bunny was a 4-issue comic miniseries that had The Justice League meet The Looney Tunes. Superman, Batman, Wonder Woman... almost lost their minds by the way. The Looney Tunes are too fucking psychotic and random for even the strongest superheroes.
I mention the cross-over for two reasons. One, it is proof Bugs Bunny has met Wonder Woman. And two, Bugs Bunny was the one who saved the day. While the World's Greatest Detective and the Son of Krypton tried to figure out how to stop Mister Mxyzptlk, Bugs actually did so by outsmarting the trickster.
So I don't think it's any stretch to say Bugs Bunny could outsmart Wonder Woman. I believe he would know how to defeat WW because he does read DC comics and was even shown doing so in that 4-issue comic.
Wonder Woman's weakness, at least originally, was being bound. Her bracelets in particular:
Bugs is no stranger to bondage. Many times we've seen him tied up with rope ready to be served in stew, walk the plank, hanged, dive into a shallow pool, etc just to escape. Guy knows his way around getting tied up, and how to get out of it. Surely he would know how to bind someone.
And it doesn't say she had to be bound by a
human man, which is sort of odd. You'd think coming from the Amazonians the rules would be more specific than that, but they're not. Comics love exploiting loopholes and that is why we have a woman Thor. Bugs Bunny is technically a man. He can subdue WW.
But I feel it is a valid argument to say the whole bondage weakness was retconned. What weakness does modern Wonder Woman have? Well she does date Superman now, and Batman even said in the New 52 that if she did have a weakness, Superman was it.
And what Master of Disguise could fuck the modern Wonder Woman's world up?
Bugs Bunny is highly unpredictable. He is a manipulator with a silver tongue and defies physics on a consistent basis. He beat a Superman villain he barely knew in the same comic that had ALL the major players in it including Wonder Woman. He could trick Wonder Woman. He'd piss her off but not before he eked out a win.
Can WW even use the Lasso of Truth on Bugs? I mean the dude comes from a world of lies.