I dont want the pump or anything with a power cord inside of the pool, so im thinking 1 or possibly 2 pumps placed inside of the bucket or 1 of those external pumps (like in the picture below)

But I think using a pump like this external pump the water would enter into the bucket and then the water would be returned to the pool from the outlet on the pump. These pumps are exspensive so I would rather not go this route if i dont have to.