Aight then. 99% sure this ends up with Salem getting a dose of Aphrodisiac, or her soul destroyed.
Bai has the AP, backscaling from 7-B and being able to one-shot hose equal to him with his special abilities.
Skill isn't a large factor at all with both using magic that have nothing to do with things like knowing how to stab someone well or such things.
Bai has better skills, with immense amounts of barriers, and a one-shot hit with waterswamp (it reduces people stronger than her to vapor, which should be beyond regenerating from being liquified, and regardless it destroys her soul too). He won't use it unless really pushed tough, and could be interrupted if killed while using it or made unable to make Naruto handsigns.
And the one and only, almighty
Aphrodisiac Pill... he would probably hesitate using it on a lady, but if pushed this would come out before the waterswamp. If she is hit by it, she
will succomb to it, after which she becomes unwanting to fight and Bai wins (no, her Grimm "hate all humans" thing can't overcome that pill, it overcomes mentality and resistances far beyond something like that).
So... voting by Bai by getting lewded.