Assume that there is no air resistance to slow the bucket down.
The cork will stay at the bottom of the bucket and not float up at all during the fall, since the cork, the bucket, and the water all fall at the same acceleration g (neglecting air resistance as all good physics questions do). The buoyant force of the water does not push the cork upward in this case, since in free fall the buoyant force is zero. In other words, a cork only floats up when the surrounding water is heavier and pushes it up. In free fall the water is weightless, as is the cork and bucket, so there is no force to push the cork to the top of the bucket.
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