When a bucket of water is just raised up and inverted, the water is strongly pulled by the force of gravity of the earth’s surface whereas there is no normal force below as there is no surface to limit fall of the water and therefore it falls
When someone rotates the bucket of water in the vertical circle, they are pushing the water away from their hand, towards the base of the bucket by a force which is directed away from their hand.
This force when balances gravity, the water would just be in the bucket. But when you spin the bucket this outward force named as Centrifugal force overcomes the gravity pull and pushes the water to the end of the bucket away from the opening of the bucket. So, it does not drop from the open end of the bucket.