How big a bucket of water would you need to put out the Sun?

No bucket of water will be big enough to extinguish the Sun. On the contrary, the more water you pour on the Sun, the more it will burn. The fire we normally encounter on the Earth, whether it is a campfire or a candle flame, is based on a chemical reaction. In the case of a campfire, the carbon contained in the wood chemically bonds with oxygen from the atmosphere and this process releases light and heat. In order for a new chemical bond to form between carbon and oxygen, the original chemical bond that bound the carbon to the beech log molecule must be broken at first. High temperature is used for this. As soon as you pour a bucket of water on the campfire, you cool it so much that the breakdown of the carbon bonds in the wood can no longer take place, and if the carbon is not free, it cannot even combine with oxygen. At the same time, water also limits the access of oxygen to the wood. But the Sun is not a gigantic pile of wood burning in an oxygen atmosphere. The sun is a giant ball of hydrogen. It is so huge that it collapses under its own weight, and there is a crushing pressure at its centre that allows the nuclei of hydrogen atoms to get close enough to fuse. While in a chemical reaction, everything takes place in electron shells and the nuclei of atoms remain intact. In fusion, the nuclei themselves participate and transform. In the Sun, protons meet and gradually fuse into helium nuclei. This reaction is enabled only by the gravity of the Sun. The more massive the Sun is, the higher the gravity it will have and the more pressure it will have at its centre. Thus, by pouring a huge bucket of water on the Sun, we would only increase its mass and thereby enable even more intense fusion reactions. In addition, hydrogen from water molecules would serve as its fuel. You simply cannot extinguish the Sun with water.