Going back to caveman times, a few hot coals were stored in a leather pouch full of ashes, allowing them to transport their fire starter to where ever they were going and start a fire the next night. Fire hasn't changed; coals can stay hot and flammable for days. It simply isn't safe to dump your ashes in an open bucket of any kind!
Any container you put ashes into should have a tight fitting lid. First, you don't want your cat using it as a potty. More importantly, you don't want any chance of that bucket turning over in your home or blowing hot coals onto your deck or into your yard, spreading hot coals or embers that could start a fire.