I played a good so far one last night and these are a few things I noticed...
Bayonetta has better 'priority' (?) in the air, it seems. She beats Yoshi's F-air with speed and other moves with unfavorable trades. Yoshi's D-air doesn't eat up her Up-air on decent like against some characters, but trades unfavorably. The same can be said for B-air. I think she has intangibility on her legs when their flying all over the place. Getting in with N-air is tough because while she is tall, she is very lean.
The only option against Bayonetta with Yoshi in decent seems to dodging and DI'ing perfectly until you hit the ground. I was having zero success in the air so it seems the MU requires Yoshi to play well on the ground. Yoshi suffers from not having a significant grounded multi-hit move. D-air is Yoshi's best grounded air attack since it doesn't get witch timed.
The guns with hit-stun are awkward for Yoshi to deal with. I imagine some characters can run right up to her but Yoshi is too tall. He can dash attack under them only at a certain distance (like far enough to get the weak hit, but not the 9%. I've also tried Egg-Roll and crawling D-tilt, but those don't seem to be optimal solutions. Run up > DJ Armor > fastfall F-air might also work, but I'm not aware of the frame data involved in the exchange.
Bayonetta can play like a witch and spin around with her non-hitstun guns and run away. While you have to approach, it should be a cautious approach. Egg-Lay is good for being safe against witch time, but it can't be spammed because it's easy to punish.
So I only know about FD, but I'd say the MU is one where Yoshi is forced on the defensive, but also has to deal with passive projectile damage so he can't camp the whole match. Walk around and shield her attacks, dash in for a hit when she's exposed. Hit her 10 times with dash punishes then find a way to kill her.
Bayonetta has a dirty combo game, but Yoshi's DJ might give Yoshi enough of an edge for it to be a fair MU, but you have to play a really calculated and technical play-style backed by crazy reads to win.