If the problem with shallow water is that you see the walls and the bottom instead of only the reflection, I would just use a black bucket. Or somehow make bucket's inners black.
Moreover a bucket is a bit unpractical in this case, just a really black tray with water should suffice.
Another option is to make water black itself, like using coffee.
UPD All three light sources should behave identically in terms of reflection provided the water/tray is really black. However in real world the brighter the light the darker color is required. I just advise you to try it yourself.
There is another matter you might be interested in. The portion of light reflected greatly depends on the incident angle. If the light goes almost parallel to the surface it will be reflected almost completely. So if you are trying to imitate a reflection of houses or trees on a river bank (tangent light) you'll get brighter reflection than if you are looking straight down into the bucket.
The logic is quite simple. When the light hits the water most of it passes through the surface, the smaller part is reflected. In deep water the light that passed through eventually dissipates and does not return back. All you see in that case is the reflected light.
In shallow water the light hits the bottom and bounces back riving with one that reflected.
So all you need to make reflections visible is to eliminate the light that comes back from the bottom. Either paint the bottom black or make water black.
However I don't think it is how I was reasoning. I've just remembered an analogous situation with windows. When you are indoors at night with room light on your windows are essentially mirrors.