In my opinion, I would go with neither.
Infernape is too frail to get good use out of Bulk Up - leave that to Pokemon like Conkeldurr.
Fake Out can be a good move, as it helps break Focus Sash/Sturdy, and is just free damage. If you decide to do this, I would suggest the Life Orb as your item.
However, I prefer to use Swords Dance instead, with the Focus Sash as your item. The Focus Sash ensures you get at least one Swords Dance up, and from there you can try to sweep. It is slightly riskier, but at least Infernape gets Mach Punch, and so is not completely shut down by priority users.
Since you are using the Focus Sash, however, you need to change Flare Blitz for something else, as the recoil will kill you, or break your sash if it isn't already broken (thanks to Crimson1 for reminding of that). I suggest either Fire Punch, which is boosted by Iron Fist, or running a mixed set with Overheat. Personally I prefer Overheat, but you can do whichever you prefer. Since it would be your only Special Attack, the stat drop from Overheat won't matter, as the rest of your moves wouldn't be affected by it.
Infernape is one of those Pokemon with several good move sets, though, so you could certainly scarf or band it, but if you do this DON'T give it either Bulk Up or Fake Out. Locking yourself into a set up move is just stupid, and locking yourself into a one-use move is nearly as bad. Give it U-turn instead. Also, especially on the scarfed set, you probably should replace Mach Punch with Close Combat. It isn't necessary, though.