This bucket is by no means unique in truth, rather many wizards have thier apprentices make one as part of a kind of mid-term exam, so to speak. It's existance used to be a secret and the wizards still deny it's existance is the result of any training they conduct, but more and more appear every year fueled by apprentices in need of cash monies.
It is missing the tell-tale earmarks of a full fledged magic item: While it does radiate something along the lines of alteration, it doesn't glow in the customary magic item fashion, nor is it even a "masterwork" bucket, indeed, most appear to have been stolen from wells, stables, or other less desirable places to source buckets from. Most all of them bear some sort of makers mark, but as often as not the mark is rubbed out charcoal or washed away entirely, it is very rare to find such an item with a mark of anyone wanting to take credit for it's creation.
In addition to it's appreance, it's function has some quirks that some would call "flaws" or "defects" or "sadistically useful". While it does indeed allow the user to breath underwater, it's only under the water inside the bucket, trying to then breath other water has the customary effects of drowning. Also missing is the feeling of breathing air, that is to say, you can breath the water in the bucket, but it feels just like breathing water, inside a bucket, and nearly everyone reports some discomfort with that. Another obvious design flaw would be that buckets are not very transparent. Wearing one as a helmet, even if you could cope with the sensation, would prove problematic in the act of navigating.
The most obvious use for such a device is to allow creatures not normally meant to be underwater survive underwater, with some discomfort. Another use surfaced with the enforcers gambling debts such apprentice wizards sometimes incur. They find such buckets indespensible as motivational tools, after all, how much easier would a knee breakers job be if they had a bucket they could use on someone to make the indebted soul feel they were being drowned for minutes and minutes without risking losing the ability to collect on the debt by actually drowning them? Lastly, an even more despicible group of conartists sell ordinary buckets as the magical ones, and woe be to the doomed soul who expects to to be saved when he places the ordinary bucket over his head and takes breath after breath of water, even when he feels the drowning sensation ...