Mosses grow well emersed on damp soil in a sealed or semi-sealed container. They can grow in unsealed containers as long as the substrate's kept fairly moist. I've got Christmas moss growing in a plastic salad take out container and some Java Moss growing on some old wet soil in a 10g. For a true DIY feel, a ziploc baggie with will do the trick too.
The Java Moss gets a liberal dosing of old tank water once a week and a spritzing every few days to keep the soil moist. My mosses are sitting directly on the soil, but if you wanted to stick them on some nylon mesh and let that sit in about 1-2mm of water they'd be happy. Mosses are non-vascular and use capillary action to transport water to their outermost regions so they won't get too tall if they're not in a really humid environment.
If you're trying to get sporangia (capsules) my hunch is they'd need to have some portion out of the water. Most mosses I've read about "ejaculate" when a breeze blows the male spores into the water where they may meet up with a female spore and produce their zygote. I doubt you'll get any sexual organs growing if your moss is more than 1/4" under water.