I've never heard or thought about bells it sounds like they would be pretty effective.

After some research, which is hard to do with most websites trying to tell you there shitty product will stop hunting better than everyone else's. It looks like there aren't any studies that say bells reduce hunting more than 50%. Most cats just find ways around jiggling the bell or they just don't walk and wait for a bird to come within pouncing range.

You can keep your cat however you want but I wouldn't be sure they aren't killing any birds, or noninvasive mammals or reptiles.