The only way to keep cat urine from eventually ruining everything in your house is with the application of the following tools/procedure:
1)inform your wife "there will be no cats in my house"
2)open the door
3)option:
a)pick up cat by scruff of neck & throw through (2)
b)whack cat with broom until it voluntarily exits (2)
4)close door
This has worked very well for me. I was kind enough to provide the cats with food & water outside, but that's up to you.
Now that we have that figured out, ammonia (a primary ingredient in all types of urine; cat urine is especially nasty) dissolves copper. That is why Barnes CR-10 smells very much like my 2 year old's morning diaper. In addition to the copper that is likely plating your bullets, the brass is an alloy of copper and zinc. Here's the rub....if the ammonia works on the brass long enough, it can do some real damage. I would clean the ammo with water and possibly throw in a little vinegar to neutralize the weakly basic ammonia. If it's not pitted, I would go ahead & shoot it, but if you can see damage I would be leery of it. Most likely the worst thing that could happen would be a cracked casing, but that could be enough to cause some damage in rare cases. Definitely discard any brass that has been corroded.
ETA: My wife washes those aforementioned diapers with vinegar in the washer as someone mentioned above. They come out fresh and clean. Yes, people do still use cloth diapers. If they get stained or smelly beyond what the washer can handle, a few hours on the clothesline (yes, people still have clotheslines) in the sun works wonders. That range bag is too nice to throw away. If nothing else, mail it to me.