I trained Zenu to use the bell as well, but I dont have a fenced yard so it means me getting her leash and taking her out for a walk. I can usually tell if she needs to go pee or poo or just wants to go for a walk and look under parked cars for cats, and if she's being silly about it I just tell her, "no you already went out" and she'll give up after a few rings. If she can be distracted from the bell with a ball or rawhide stick its a pretty clear indication that she doesnt really need to go to the bathroom, she's just bored and wants to do stuff.
Usually she doesnt even need to ring it since we're on a good routine of walks throughout the day, but this morning she had a bit of diarrhea and she woke me up at 5:00am and ran right to the back door and rang the bell several times to let me know it was Very Serious and Can We Please Hurry.
So, even if you ignore him sometimes when he rings the bell, he'll probably still ring it to let you know if its a real emergency.