I don't frequently have peppers from the garden sit around more than 3-4 days. The time sitting on the counter may have been sufficient for that particular pepper to go bad. Unless the plant appears to be producing rotted produce, I would chalk this one up to a statistical anomaly / too much time on the counter. That said, ammonia is an odd smell to get from a rotting pepper; though not uncommon with other foods (e.g. mushrooms).
I don't know if too much nitrogen might be to blame for the ammonia smell (i.e. there is nitrogen in ammonia, thus ammonia smell is from too much nitrogen; but that's an inversion of a logical fallacy). Still, it seems to be the likeliest first step in a more detailed diagnosis if the plant continues to produce fruit that smell like ammonia when they ripen. Are you sure ripenening color was appropriate to the cultivar of the pepper? If you picked it too young the resultant bitterness, then ripening could have forced some odd, under-ripe flavors.
Were you having any sinus issues when this occurred? Do you suffer from post nasal drip, acid reflux? Or, did you have independent confirmation of the ammonia smell? Sorry for the health questions, but I'm curious and trying to approach this from a different angle. If you have independent confirmation, nevermind; but if you suffer from these things occasionally, there may have been something that caused a flare up and resulted in these things stimulating an ammonia-y experience.