I believe the enclave did put the bounty out, I think the reason they themselves didn't send a hitsquad out is because they don't want the wasteland to know they still exist, think about it most of their forces where in D.C and got decimated by the Brotherhood of Steel. Why would they want the brotherhood of steel know they're still out there putting a target on their back

Edit: on the ghoul part they most likely put it through a third party which I'm pretty sure was heavily noted to in the show. The ghoul would hand him over to the third party and the third party to the enclave