Please DON'T load ball bearings in any gun that you care about. They are way harder than the steel of your barrel. They are made super hard, so they can roll in a bearing for thousands or revolutions without wear or deformation. If just one ball bearing was not completely protected by the shot cup during its trip down the bore, damage to your barrel and choke is guaranteed. Steel shot used in waterfowl loads is made of specially soft steel, and even then some shotguns can't digest it without damage. People found out about loading shot that was too hard when some geniuses tried loading loading air gun BB's instead of proper shot shell BB shot. Bad move. I'm not sure about the hardness of slingshot ammo, but I wouldn't risk it.
Remington and Federal make some tungsten alloy buckshot that is factory loaded in special shot cups. That stuff is as hard as ball bearings, but they use special loading techniques, and the components aren't available as far as I know.