Dexter isn't much of a barker in general, but I swear the cat aggravates him on purpose to MAKE him bark. She sits on the other side of the baby gate and provokes Dex til he loses his mind and starts barking.
Dex has an Iris pen with his kennel/bed in it and when he won't stop barking we tell him he has to go to bed. The first couple of times, I just popped him into the pen, told him firmly 'Quiet Dex' and left him for 5 minutes, then let him out. He ran straight back to the gate and started barking again, so I picked him up, repeated the 'Quiet Dex', popped him into timeout for another 5 minutes and let him out. That was enough for him, no more barking and he gave up on the cat
Now all I have to do is say, 'Quiet Dex, you want to go to bed?' and he quiets and runs, I rarely have to timeout him now.
I don't mind the quieter little 'oofs' he makes when he's being tormented by the cat, just the loud over-excited barks earn him a timeout. I also don't shush him when he hears an outside noise because I consider that his protective warning bark.