Matthew,
Officers are sworn to enforce the law, even if they themselves don't think it makes sense (been there, done that).
If city law says "No discharge of a weapon" then bows, paintball guns and even beany-flips apply.
The officer probably could have written you a ticket, or even arrested you.
Sit out front of the house and wave him down next time you see him. Appologize (and mean it!) for having possibly committed a violation and ask if he knows of any place close to practice. He may bowhunt himself and have a great place to shoot. At worse you still have to make a 5 min. drive to practice and you stay in the "good guy" column with him.
He backed up because he decided he couldn't let it go. If by some freaky accident you did some sort of damage or, Lord forfend, hurt someone, what is he supposed to say? "Yep, saw him doing that but I figured he was okay."
If there is a law and you don't like it, get enough folks together and change it. If the law says it's OK only at an approved range, get some folks together and have the city designate a range.
The guy was just doing his job. If he had over-looked something that you didn't want your neighbor doing (and it was against the law) the shoe would be on the other foot... so to speak.
OkKeith