Basically, the water would be held inside the bucket in the shape of the bucket without getting the bucket wet, because the hydrophobic coating would prevent the water from touching the bucket, however the water would still touch the hydrophobic coating, it just will not stick to the hydrophobic coating.
Eh nothing interesting. The water would be in the bucket but pool and bead much quicker, instead of spreading and getting the bucket 'wet'. Kind of like a hydrophobic windshield coating.
The water sits in it, but only where gravity holds it. There would be a very pronounced meniscus at the top. That is, if you looked closely the water would dip down really far at the edges before it meets the bucket.
It's not that hydrophobic substances can't touch water, it's that the force of surface tension will oppose it. Unless you're an ant, surface tension isn't that impressive vs. most other forces.
Edit: If you have an ant-sized bucket, the water may sit on top of it as a droplet rather than going in.
I think with a jump and just the right angle of entry you can probably slide down the sloping face ...and probably end up with two broken legs and a tap half-way up your asshole.
Basically the same thing as when you fill a non-stick pan with water. Hydrophobic coatings only repel water in a way so that it doesn't stick to the surface. That's why they use hydrophobic coatings on windshields, so the droplets of water slide easily and quickly.
Granted, the effect is more noticeable with hydrophobic coating than with non-stick coating, but if you were expecting the water to visibly float away from the walls, that won't happen with either. Reality is sometimes disappointing, huh?