It’s easier to clean up resi-goo in one bucket than it is all over the floor. Especially since visitors to that ensign’s quarters wouldn’t be expecting to see goo everywhere. At least Odo’s visitors wouldn’t be surprised by it.After his encounter with the Founders, Odo stopped using the bucket and got himself assigned to personal quarters; he would instead revert to his gelatinous state and shapeshift freely throughout the room, allowing himself to spread across the floor when he needed to become gelatinous. Odo kept the bucket with him "as a reminder of how [he] used to be." -- https://memory-alpha.fandom.com/wiki/Odo's_bucket
The writers forgot that a bucket was an Odo thing, not a Founder thing, and even Odo himself gave it up after a while.
At least that’s my head canon.