Megaman has metal blade, which beats out all the movement specials IIRC. The followups from this can be pretty threatening, since you really don't want to get baired by the ledge, especially at bayo's weight. Z drops in the ledge area are great for pressure since you have great room to vary the timing + use aerials/pellets to supplement the pressure. A MB stage spike won't kill the witch outright, but you can jump on the chance with some bair/nair action and hope you snagged a jump and get repeated stage spikes.
Leaf shield can apply some pressure in a weird way, such as putting it up then snatching the ledge from bayo... But I'm pretty sure a bayo adept at planking takes the ledge before you, or just stays low then WT the ledge when you lose your grab invincibility? If grabbing the ledge quickly was an option, everyone could beat this, so I'm assuming it isn't doable against properly executed planking. In general LS is pretty **** in the MU due to the ease of Witch Timing it, and getting hit with it and not having access to Rush immediately is really scary. So it having a little use on the ledge is a neat little mention, but honestly I don't think its worth using vs Bayo's massive limbs. Rush can make things very interesting, you can use a rush planted right at the edge to cancel the landing lag from anything, and bouncing off him to go offstage to fight is a decent choice since you get your jump and another rush back. You can, for example, space a FF dair to hit the snap zone and still get a rush bounce with proper weaving.
All Rush strategy is high risk high reward if you both decide to bounce up there. Megaman has his infamous uair kills, which will kill Bayo WITHOUT her panic jumping at such a height. Bair can also provide some early kills, DI up kills you and DI out optimally can still kill earlier than normal.
Crash bomber... Meh. To get it to stick to the ledge, you have to go well into the danger zone, so its really really not worth it. Sticking her can put some quirky pressure on her; if she times her stuff wrong it can either stage spike her, or you can go out there and get a bair (at kill %) or uair (below bair kill %) combo off the CB.
"Fun"... fact, bayo can Witch Time the (non damaging, may I remind you...) stick from the CB impact. This really disappointed me upon learning, because CB was supposed to be a nice way to pressure her without threat of dying for shooting a 2% pellet... She can WT the explosion of course, but if you get a stick you could either dash back or Rush into the air for safety.
So metal blade and Rush are the best options for specials. Normal I can also explain if anyone wants that, but they are more universal/obvious. Bair is a strong disjoint, so hit her with it. Dair is actually pretty unique, disjointed projectile spike, which is also a decent option vs Bayo.
Oh, and this is a situation where MegaMains are actually GLAD to have charge buster for his fwd smash! I'd still take it at 0.15x power, stored to be shot at the opening to a pellet salvo :]