The water is strongly pulled by the force of gravity of the earth’s surface when a bucket of water is just raised and inverted, whereas there is no normal force below as there is no surface to limit the water’s fall it falls.
When someone rotates the bucket of water in the vertical circle, they push the water away from their hand, towards the base of the bucket by force directed away from their hand.
This force, when it balances gravity, the water would be in the bucket. But when you spin the bucket, this outward force named 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.