I have been growing out BBS for weeks now. Both to feed my baby bangai cardinals and supplement the feeding of my mandarin. I also kept cultures going for years when I had small shell dwelling African cichlids.
I grow them in one of those silly Wallmart 2 gallon bookshelf tanks. Why? Because I had them. I have used commercial built hatcheries, soda bottles, you name it. Other equipment includes a simple and small air pump, hose, and no stone (the cysts will adhere to the fine bubbles, to float to the top, and when the bubble bursts, they often stick to the side of ANY container you use. Much like a skimmer).
I use no heater, but keep a 60 watt desk lamp DIRECTLY over ( I mean an inch) the water surface. Light is important during hatching. It also helps to keep the water temps slightly above room temperature. I use a piece of plexiglass to keep the salt spray off of the light.
The key is to ensure you have decent eggs. Cheap, old, or damaged cysts have a low success rate. Buy fresh, vaccum sealed brine eggs and keep them dry. If you've got some cash to throw around, you can buy de-capsulated cysts. You can also find recipes for doing this on the web. I don't find the shells to be that much of a bother. They either float to the top or settle to the bottom when you stop the water flow. Ensure that the water in the breeder is rolling, like a good boil, but not too strong where the eggs come out of the water. I use a simple brass valve in line.
Because baby brine are not the best source of food (especially after the yolk sack is used), I feed my hatchery with Phyto-Feast Rotifer Diet and essentially "gut pack" them before feeding my fish. I put just a few drops in, turning the water green, and within a day, the water is clear again.
I use a siphon and brine net to collect and feed my system(s). I replace the water with water from my fuge, and replace the fuge water with fresh IO/RO/DI. I scoop floating and siphon out settled shells during this water change.
I break my culture down every two weeks to clear it of cyst shells, debris, etc. I have shrimp in there that range from newly hatched to some larger adult size. Funny....how as a kid, I cried when my "Sea Monkeys" died...now I breed them to eventually send them to death row... a 75G reef.