Saying Big Mom would bail out is flatout shitting on her character. She's as prideful as Kaido and Whitebeard, no way she's running away
Big Mom will be defeated here even Oda knows that we can't withstand another arc with her. Big Mom's purpose here is to make Luffy stronger, while Kaido will be probably taken down by Luffy and Kid "based on narrative factors" whith small assistance from other supernovas.
On the other hand Luffy takes down Big Mom in 1v1 since he numerous times said that he will defeat Big Mom after Kaido.