There are thousands and thousands of kinds of moss. Unfortunately for non-bryologists, we can't tell the difference between the different species, but it doesn't matter. I bought two handbooks on moss, "MOSSES, And Other Bryophytes", by Bill & Nancy Malcolm, which is probably the definitive manual, especially if you routinely use your microscope, and "Moss Gardening", by George Schenk, which is book about using the different mosses in different applications of gardening. You buy the first to study moss, the second to use it in horticulture.
Moss is endemic, everywhere, just different kinds. It almost doesn't matter because to the ordinary mortal, they all look alike. They spread by spores which mature in the sporangium, the tiny little nodding capsules on skinny threads that grow above the Moss and are released in the breezezs. Be happy when you see these in your Moss, -that's next season's green blanket. Moss is not forever, but just like evergreens, they have new greenery growing in-between old greenery before the old dies, so they look like they live forever. For bonsaiists, the most important distinguishing characteristic is; you need to collect it from the same conditions that you intend to use it in. If you want to use it in a sunny location, collect it from a place that gets sun. If you want to grow it around trees that need complete shade, you can get that in a forest. If you collect forest kinds and put them in a sunny pot they will immediately perish. Sun-tolerant moss will just fade away in the shade.
Mosses and Lichens are substrate-specific: they grow mostly on cellulose, so some on concrete, some on old shingles, wood, bones, bricks, rocks, etc., and that's important. Assume that you have to put it on the same kind of substrate you found it to be successful. If you find it on an old shingle, just take the shingle home. Moss doesn't have roots, but it does have "feet". Try not to damage the feet. Use a thin metal spatula to pick it up. You can keep it on a tray like they use in a cafeteria for a year or more. You can find Moss for most bonsai purposes in places that are not disturbed for a few years. The best are the parking lots of business or industrial buildings that have been unocupied for years. It is important that the snow plows have not been there for some years. The rules of Moss hunting for bonsai are: it likes some shade. The best exposure is 1/2 day, either morning or afternoon, on either side of a north-south running wall, fence line, tree line, etc, or north of a shrub or low tree line as along a curb running east-west. They need more water than the area gets, in general, such that they are where the rain drains to. A little bit of dirt is helpfull, but not much dirt, -just a scrim. It needs to be to shallow to not support the weed seeds that germinate there. The Moss will be happy with rain, drought, rain, drought, rain, drought, but the weeds that greminate will die. There will still be lots of weed seeds hidden in the Moss, that's fine, since Moss doesn't have roots you can spray it with Round-Up. Caution: give it plenty of growing time to flush the residual Round-Up out of the system before you put it on your bonsai, or else. Look along curbs, at edges of sidewalks or parking lots where the earth is slightly higher than the pavement and soil has washed out onto the hard surface and that surface is where the rain drains to. Any place where there is a seam in the pavement that has opened up and soil has washed around a central drain, or down to another seam where one side has risen and blocks soil and water. After a while, you'll be able to drive past a good candidate at 60 miles and hour an spot it out of the corner of your eye.
Don't take it all and it will regenerate so you have a continuing supply. The older clumps are nice, but to apply in some situations, you need just the beginnings of Moss growth, like a green stain on the soil. That is really hard to handle, -collecting it breaks it up, tansporting it on the spatula to the tray, putting it on the pot surface. It will, however make a nice carpet soon after your put it in good conditions, so havest that too, when you get the bigger buns, because you'll need it to fit in small spaces without covering up roots, etc.
You can over-winter it on trays, too, and it will look better than if it were covered with mulch all winter. You can screen it into dust and keep it in a jar a long time. Apply it with a salt shaker to a unbroken surface like a slurry of chopped dry leaves you can stir into water until you get slimy glop. Lichen can be scraped off a surface and salted on another surface, but remember it is substrate-specific so if you have an iron bearing rock source, it has to go on the same kind of rock. Tree Lichens same thing: Maple-to-Maple, Beech-to-Beech, ad infinitum. Good hunting!