If you anticipate Headstomps, you can beat them with Neutral Jumping Roundhouse from almost any range.
Long range is the worst as Bison will be heading more towards a Neutral Fierce hitbox (lower) than Roundhouse’horizontal (sideways) box but it can still work at times but at this sort of range a grounded normal is much better anyways - Best used at mid range or close if you’re hella good at reacting to it or anticipating it. Love this against Bisons who just have a habit of opening rounds with Headstomp Devil Reverse meter building and happen to sail into the middle of the arena.
Bison without meter = Can be thrown out of all his normals and specials on wakeup (yes, Scissors and PCrusher) and I find the result of the match heavily boils down to who gains the lifelead via being aggressive at the start and preventing meter building (Not a breeze for Balrog if Bison has range and loves to spam DR’s at long range - If this is the case, you may as well light headbutt anytime he uses a DR to build meter as well).
Bison hasn’t a lot of wakeup options of any real use when he has no meter, also, so I like to mix it up between regular jumpins, jump overs to remove his charge and tick throws to catch him trying any specials (see above).
If you’re going for meaties on wakeup, crouching forward is exceptional - If timed right it will not be hit by wakeup Ultra 1, SKs or EX SKs, PC or EX PC and because it’s such a lopsided move with weird startup/recovery you’ll recover with plenty of time to react to anything else being thrown out, such as backdashes (Sweep or FSJab) or HS / DR’s. Best case scenario it’ll hit, stuff or counter hit for a free combo when he has no meter or doesn’t use Ultra (Sweep or BnB of choice, CMK CJab CShort Headbutt, CMK FSJab Headbutt etc) or simply be blocked into a decent block string. If he does use an EX move CMK will whiff and you will still block.
I find at mid-range, SForward, Roundhouse, CRoundhouse are decent normals for stuffing SK’s when you are advancing and don’t be afraid to neutral jump if he has backcharge but no down-charge - Bisons love to throw out SK’s on a chargeless Balrog trying to get in on him but this will lose to Headstomps or PCrushers if too close while you are falling, if they fall for it, free BnB or Ultra combo from Neutral Fierce.
If you do get in on Bison with a UTK but he’s not in the corner, abuse cross jumping so he loses charge - Bisons under pressure will be looking to use EX PC or SK’s to get away, take this from him.
When he IS in the corner it’s highly likely they will wakeup EX PC if you’re extremely close to get out of the corner, in which case I often try my luck with a backjump fierce on their wakeup which’ll hit him out of it and keep him back at the corner - Failing that he’ll whiff and you’ll be in range of a sweep even if he does get out of the corner. In short, if you suspect a desperation EX PC escape (or if you notice the Bison does it all the time when cornered, try it, you’ll likely hit him clean or if mistimed, trade).
If you’re not playing AE (I’m still playing Vanilla) I like to mix in headbutt crossovers if I don’t feel like jumping over Bison on his wakeup. This builds meter and can be mixed up with light or heavy headbutts to either go over him or stay infront of him and test his blocking. Not the best option but it’s something.
If for some ghastly reason he uses U1 and you block it, hold up-back as he’s passing through you and you’ll jump at him for a free combo punish.
If Bison teleports your jumpins, there is a TAP option select where you’ll hit him on teleports - Failing that, if you predict one, you can even walk forward and just sweep him.
All I can think of at the moment.