Though to be "realistic," Pinky will probably make Bugs her friend before she gets tired - that's basically her main power, and we know that Bugs loves a party.
Note: My 5 year old daughter loves MLPFIM, and Pinky is definitely her favorite, so I could be biased. Little princesses do that to their papas. :-)
Alternatly she annoys him so much by trying to be "friends" with him, that he goes into the agressor role and starts behaving stupidly.
From what I hear of Pinkie Pie, I think Bugs steamrolls by virtue of not only being the king of all toonforcers, but simply having a superior and larger library of feats of all sorts than her. Does she have anything that can top being the god or artist/writer of your own cartoon/work and erasing/humiliating your enemy from outside for the lulz?
She has MUCH better Disguises than him.
Bugs's idea of a disguise
Pinkie Pie's Idea of a disguise
Given Bugs's tendancy towards "mistaken identity for someone in a disguise" gags, Bugs could very well end of harrassing the REAL Fluttershy, and either getting EVERYONE mad at him, or bringing out the Flutterage.
Looney Tunes-level toon-forcing is far above anything in the MLPFIM-verse.
Even Mr. Mxyzptlk wasn't a match for it when he visited the Looney Tunes-verse. And he's a wee bit above someone like Pinkie.
During a DC/Looney Tunes crossover when Mxyzptlk and the Do-Do met and merged their worlds together. Mxyzptlk checked out the DoDo's world first and got walked on by pretty much every one.
far above anything in the MLPFIM-verse?
For something as big and awesome and legendary as looney tunes/warner bros-level toonforcing, that's really underrating it imo. try "infinitely".