What gun would be the best

I'm assuming you dont live in an area where guns are common or are shot frequently. Guns are very loud, up close. Even in the middle of nowhere though, most calibers are small enough that a half mile across open field is difficult to discern where the noise is from besides a general 'I think that's over there'. In a quarter mile of houses or heavy woods, you can get the general 'it's that direction.'

Next, the level of training it takes to be proficient with a bow against a moving target is insane. Arrows do not travel in a straight line, it has to be compensated for with each shot. Bows all have different draw weights, what works with one bow might feel very different with another- recurves, longbows and other traditional bows especially. Each arrow is going to have slightly different mass and air resistance, that changes its flight dynamics- especially for someone making their own. Hunters use bait for two reasons, the first is to draw an animal to a single location, the second is to put the target in an optimal spot to take a clean shot. That clean shot is against game that has stopped to eat. Zombies arent going to sit still for that, especially if there's someone panicking and shooting arrows at them.

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