Okay so uh, working your way in is obviously pretty good strat. Walking him to the corner is tedious but patience is key once you get there. If you just start pressing buttons he'll take a chance to F2 you, DB2 you, MB roll away or anti air you if you try that route. Fate cornered against Bane is a very poor place to be, Fate has no wakeup options that are able to break armour or are throw immune I believe.
Beating MB orb - obviously hard. Waiting is a pretty easy way but he'll begin building ankhs once he realises you're not going to do anything. D1 goes under MB orb pretty well if he's sitting right up against. Any distance further and jumps and MB rolls begin to work more consistently since it doesn't check them for Fate unless the orbs are point blank.
Dealing with DB2 or F2 - Obviously armoured reversal is an option to stop Fate from somewhat looping these, but as ALWAYS, risky as fuck. Fate going for a D1 is hard to deal with since your fastest option to try and challenge him is your 11 frame D1. DB2 is -8 on block so that means his D1 comes out at 16 frames, so doable but sometimes the block stun is a bit tricky. MB and traited DB2's are a different story, they're both something like -3 (something safe and I am pretty sure jails his D1 for sure).
Using grabs in the neutral space where fate might consider a F2 is a good option since grab whiff recovery is pretty decent, especially considering Bane can cover his own whiffs with an armoured reversal on anticipation of a punish attempt.
So, basically, walk him to the corner and do everything in your power to keep him there. Fate's wakeup options are very minimal in the corner and I find beating his backdash on wakeup pretty easy(ish) compared to others i.e Batman/Catwoman. Accept that getting zoned out is a thing but don't be afraid to use armoured raging charge at that sort of mid screen space provided he doesn't have an orb up.