Much of a bow's noise comes from the vibrating string after the shot.

For just a few bucks you can install some string silencers (rubber whiskers are probably the cheapest) that will reduce the noise level greatly, IMO.

I am a big fan of the Limb Saver mushroom shaped gadgets, too, but they don't seem to contribute as much to overall noise reduction as do the simple string silencers like rubber whiskers (the Sims string leaches do work well too, but are more difficult to install than whiskers.)

Good luck and have fun!