It would take a fair about of water to push it through that force.

Um... Styrofoam cup filled with water by example.

I've tested this by opening the door and shutting it faster than the speed of light.

The bucket does float. If you place it gently into standing water (i.e. no waves) and hold it still for a few seconds before letting it go, it won't sink. The average density of the bucket filled completely with water will be slightly less dense than the water itself, and that small percentage difference is going to be the percent of the full bucket of water that you will see remaining above the water (see problems relating to the buoyancy of icebergs, for example).

If you drop the bucket into the water from some height, then you're giving it an initial force when it enters the water, and that initial force is much greater than the buoyant force, so the bucket sinks.

i think he was wondering why the bucket doesn't float on the water put into the bucket...at least that's what I gathered from the phrasing of his question. Unless he's asking why it doesn't just float upwards...in which case the bucket and water is still more dense than the air surrounding it

Oh god, I hadn't even considered the possibility that the question he was asking was that stupid, haha

i know i was a little taken aback too