I have mixed feelings about this. There always have been and always will be people who are dead set against hunting. I don't think there's any point in dealing with people like that. It probably just makes them happy when they see us get aroused, like someone is finally paying some attention to them.
And if you do decide to react to what they're saying, like a rebuttal letter to the editor, you have to be careful how you phrase it. Of course, being in California, we get lots of anti-gun press from time to time, and then there's the usual flood of reaction from the pro-gun side. Some of the letters they publish from the pro-gun side probably hurts the pro-gun side more than it helps them. I sort of cringe when I read some of them, and think that some anti-gunner is going to cut it out and use it as an argument as to why more gun control is needed.
So you sort of have to keep your intended audience in mind. You don't need to preach to the choir on the hunting side, and it doesn't do any good to preach to the choir on the anti-hunting side. It's a lot like presidential politics; it's that big group in the middle that really doesn't give a darn about hunting or not that's going to win it or lose it for us.
I'm sure that was the case some years ago when they outlawed mountain lion hunting in California. There never would have been enough votes from the anti-hunting crowd to pass that thing. I think the message never really got to the middle, that mountain lion hunting was going to continue whether sport-hunting was outlawed or not; that it was just a question of whether the state made money by charging people for sport hunting or had to pay professional hunters to cull out mountain lions. Instead the message was how unfair it was to run down the mountain lions with dogs, how nobody hunted them for food, how noble they looked, and where was the sport in that?
So what would be an effective message to those who don't hunt, and never plan to hunt, if you want to preserve hunting? Well, there are several things I can think of:
The group you're aiming at doesn't really think hunting is awful, they just don't want to do it, and they don't want to get shot by accident if they take a walk in the woods. A lot of people in that group may do other things that are under attack, like motorcycling or even smoking. I think a case can be made for preserving the rights of others in the hope that they will return the favor when it comes to your rights.
Another angle is gun ownership in general. While most of the gun owners in California don't hunt, I can guarantee you that they feel very strongly about their right to own guns for self-protection, and despite a few enclaves on the coast, still are very much in the majority in California. If any move to oppose a ban on hunting is linked with the right to bear arms, you will get a lot more support than if you limited your appeal to hunters. And I doubt that you will find many people who are rabidly anti-hunting among those who want to own firearms for self-protection.
As far as bow hunting in particular is concerned, I have to relate a humorous story. For years, people in Marin county, just north of San Francisco, have had a deer problem. There are far too many people around there to have a rifle season. I have visited people in Marin county who are the typical vegetarian hot-tubbing liberals you might imagine, who have begged me to bring my bow and shoot some of the deer that were eating their precious shrubery. I have declined, because I don't want to end up in jail, but I have been tempted. One of my friends, some years ago, was head of California Fish and Game, and got tired of the complaints from Marin county people of the deer problems up there. He proposed a bow season for Marin county. His proposal was raked over the coals, of course, and I think they decided to offer the deer free condoms instead, but he thought a deer season in Marin county would have been a good idea, and so do I.