I've tried hairnets and lots of things to tie it down. Now, I use a synthetic mesh I bought at Wally world in their fabric section. It is a nice green color mesh maybe used for dress making. It was like $2 for enough for 50 rocks! I tie it tight enough and the Riccia grows fast enough that I don't think a fish could swim in there, much lees strangle themselves. Hairnets may be a different story.
One key to successfully keeping riccia looking good is regular trimming and keeping it short. If not, the stuff underneath will start to die and it will release from whatever you attached it to in a big mat. It is definitely not a low maintenance plant when growing well. But, it can be so beautiful it is worth it.