I use the toe of an old sock over the tube, held on by an elastic/rubber pony tail holder. Panty hose would work fine, too, maybe a bit cut longer so the water hose would fit down in there without having to remove the panty hose every time. I started to use one of those mesh onion bags myself, but mine seemed like the mesh wasn't dense enough to keep mosquitoes out. I do have some Bt bits/mosquito dunks, and I have read some people use them, but I wasn't sure if it would really be good for the plants and not sure I want it in my food. I guess it would be okay, though; it's just a bacteria. Still, I don't want snails, frogs or snakes in there if I can prevent it.
Before I put the box together, I cut a piece of mesh screen and glued it over the drain hole on the inside with silicone. With any pressure (pushing up from the outside), it will come off, as the silicone doesn't really stick very well well to the box, but it does keep it in position, at least for now. And someday if it gets clogged up with potting mix, I'll have to redo that anyway. But I figure it will hold off the mosquitoes and other creepies for a while, hopefully.