How about because (when he's the Bob we all know and love) he hates being like that, so he was glad that Harry wouldn't be asking him to keep flipping back and forth in order to plumb that side of him for knowledge?
It's already clear that Harry won't be doing that before harry gives him the specific command to have those memories sleep with the fishes, though.
To me, it seems like an order, once given to Bob, is permanent, with the exception that future orders can counter previous ones. So if he was so ordered, then it would take an order from a future master to overrule it, potentially giving Bob a much longer period of time before the memories arise again.
Except that it took very specific and direct orders from Harry to bring those memories out in the first place. They're not something it appears that Bob does not have under control or has to worry about slipping out in the general run of things.
The difference between Free Will and just Will seem somewhat ambiguous, though. We know that Bob does have Will, just not Free Will. So with the understanding that whomever holds the skull controls Bob, once the skull is put down, who's to say that Bob cannot use Will to pick between two equally valid owners? Cowl did hold him last, but Harry was closer and actively seeking to reconnect their bond.
That model also works, I'm not arguing against that. I am arguing that a) it is not the only model that works, and b) precisely how non-free will works and what Bob has in that context is really pretty murky sfaict so i am reluctant to base arguments too strongly on it.
How could he fake any of it? If he cut off all of his relevant memories, then he wouldn't have anything with which to fake.
He's very intelligent, knows a great deal about magic theory in general, and, depending on when Cowl asks him what, could well have any information he can gain from watching Grevane perform the Darkhallow to call on. Even without that last, it does not stretch my suspension of disbelief that Bob would be smart enough to make up a plausible means for the Darkhallow out of whole cloth.
More to the point, why would he even want to fake it, given that that would be disobeying his master, the one who was holding his skull?
We know that becoming Bob's master is not just simply an issue of whoever last handled the skull; otherwise, there would have been issues with Murphy in "Something Borrowed". I do not believe Cowl is ever Bob's master; every other change of master that happens to Bob occurs when the previous master is dead, and I can totally believe Bob still being bound to Harry and faking it for Cowl.
What was your theory for why he didn't just take Bob right then?
In GP ?
if you think Cowl actually wants to carry out the Darkhallow, well, it takes a lot of preparation. It needs the Erlking book to be found, it needs the exhibition of ancient Native American stuff that Corpsetaker is preparing in the guise of Bartleby as a source of ancient zombies, it needs the boundary between Earth and the NN to be ripped up by the tormented ghost stuff in GP. (Which, come to think of it, indicates that somebody might well have been working in Darkhallow prep prior to GP; the tormented-ghosts plan is kind of overengineered for merely getting Bianca's revenge on Harry, it has a very specific side-effect of ripping up the boundary, and mavra is right there as a suspect.) Cowl expresses active disdain for Kemmler and the Kemmlerites, and what we see of him elsewhere has no necromancy involved, so I can believe he has no real need of Bob until his plan is ready.
If, like me, you believe that Cowl and probably Mavra played the entirety of DB primarily to have the White Council take on Grevane and Corpsetaker and secondarily to mislead the Red Court into thinking they were about to have a necrogod ally, therefore over-reaching by trespassing on Faerie under the impression they were about to obliterate the White Council, and ensuingly getting the living daylights kicked out of them by Summer in PG, then Cowl leaving Bob with Harry makes even more sense as not tipping his hand and leaving all the pieces in the right place.
I'd also note that one consequence of the "Cowl was associated with the Justin/Maggie/Lord Raith cabal" notion is that it could mean Cowl has known where Bob is all along; first through knowing Justin had him, and then through knowing Harry had survived and the Council had not destroyed Bob. (From what Luccio says about Bob in SmF, finding he had survived Kemmler's defeat after all would have been major news in the Council, so the lack of that news when Justin dies would tell Cowl someone else had retrieved Bob, and Harry's the logical prime suspect.)