you are right, it is your formula a), as there is no thrust of the flowing water against the bucket, although the official NASA formula for the rocket chamber thrust implies that there is.
Imagine that you instantly open the bucket floor, would the bucket jump to equalize he momentum of the flushed water?
If I'm not mistaken, this problem is related to the rockets thrust in vacuum. It is a taboo unfortunately.
The rocket equation, ie the thrust equation, (https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation) is good if an astronaut would be throwing weights out into the space, one after another. However, the heated gas in the rocket chamber escapes through the throttle (ie adiabatic free expansion) into the vacuum without any work done against anything (including the wall of the chamber). Also the center of mass of the gas remains near to the chamber, as the gas molecules quickly go in every direction including in front of the ship, as its volume goes to infinity and pressure to zero.
So, the hot gas simply escapes the chamber (it is not pushed out by the ship) not pushing anything and not doing any work, similarly to the horizontal outflow of water doesn't push bucket in the opposite direction, or in the original problem of this tread, the leaking water doesn't push the bucket upwards.
To be precise, in the buckets examples the flowing out water does perform a work by pushing the air around the hole, but this is negligible for this problem.
So the question was: "does the outflowing water create a thrust on the bucket?", and I think the answer is "No". The answer accepted above doesn't answer the question, it rather explains the diminishing weight of the bucket due to the leak, but that was not the question.