Right. Athletes routinely sniff ammonia to give them a flash and improve their performance. But too much too often, and it causes brain damage. So while we do have to be cautious about ammonia, we shouldn't be paranoid about handling old urine.
I haven't kept my urine long enough to know what happens, but I imagine the ammonia will evaporate with time, even if the bottle is closed if it is not hermetically sealed. It will be interesting to see what happens.