I think this falls under the Diana Walsted idea, that you try to create a self-sustaining ecosystem. I suppose you should change out some water once a week or so, but I wouldn't overdo it as you'll remove Co2 and other nutrients, respired by fish, fish waste and the like....that is, if you're not planning on using Co2 and fert dosing.
Just put it on a window sill that gets sunlight for a good portion of the day, say 6-8 hrs.
FWIW, I have some java moss just floating in a flat rectangular tupperware (~6"X3"X1.5"). I top off with my tap water which is hard so it must have minerals, and add nothing. The light it gets is filtered through a translucent blind.
It grows slowly, very slowly, but it grows algae free.
i have actually done this by putting it in a clear tuberware and let it stand on top of the glass top of my tank. The spill out of light up into the tuberware appeared to be enough to keep the moss growing. It grew slow like taz stated, but was algae free. I just topped off with tank water and a little tap water from time to time to keep it wet.
I have a 2.5g jar with ricca floating an java moss, bladderwort and some java fern in it. No filter just snails and an eastern facing window with a larger overhang from roof... It pearls like crazy in the morning. Just been toping off with RO water with no WC in the last few months... Just to give you an example.
You might also want to try to grow it emersed! :icon_idea
Put some moss in a glass or plastic jar with a somewhat open (clear) lid or plastic wrap topping and let it sit in a little bit of water that will evaporate slowly. Put the container in the indirect light. I might put some sand on the bottom so that the moss would have a moist substrate once the water level sank. Most of the mosses would probably grow faster this way, and only a couple of species won't grow this way (as they are completely aquatic).