How does Bella fight Big Band?
Tumble Run outside of his c.hk range is your friend. It'll soak Brass and Giant Step, after which you can cancel into either Runstop or a super to punish him properly. You can runstop at any point to try and fake him out, get him to commit to something (just make sure you do it outside c.hk range).
Don't jump unless you're in range of his grab/lk a-train or inside the unblockable range of hk giant step to avoid getting scooped by mk/hk a-train, no reason to anyway really. Just stay on the ground. You can jump if he's in the air or knocked down.
Outside of his c.hk range, you can relatively safely pressure with mp/hp lnl. He can predict with c.hk or parry, but it shouldn't be that big a deal most of the time. I guess just use it sparringly if he's got good parry or c.hk reactions.
Titan Knuckle and c.hk are good pokes, though Titan Knuckle can get stuffed by brass and Beat Extend, so don't be predictable with it (If he isn't pushblocking Titan Knuckle, canceling Titan Knuckle into lnl nets bonus pressure).
When he's in the air, be careful of using tumble run or lnl, as cymbals will break it. However, Big Band is high enough that he can't see what you're doing at times, if such is the case Tumble Run into lvl 3 can lead to a nasty surprise when he lands and tries to punish.
MGR is an amazing poke, works point blank so any move can be canceled into it to reset, beats nearly every option he has outside lvl 3 and h beat extend.
Don't be afraid to Devil Horns if he's in your face, he's so big that he'll get hit most of the time.