Mine 'graze' the drops of rain/dew on the run mesh.As for birds drinking water droplets, very common!
As for the bird jumping on the bucket, knock her down, 'peck' her head, be the boss.
Might cover the bucket top access with a cone that is easily slid up for you to fill.
One of those dog 'cones of shame' come to mind, a large one. They usually have them at TSC.