You don't have to worry about the BSF grubs reducing the volume of high cellulose items like grass and leaves. They're only there for the kitchen scraps. If you can't eat it the BSF can't either.
If the mesh you place over the compost is 1/4" or larger the BSF adults will get past it. Even if the mesh is small, if it's close to the pile the BSF will simply lay their eggs on the mesh and the new grubs will drop in to the pile. Newly hatched grubs are only 1mm long and thin as a thread.
One thing I noticed about my collector is that the grub would migrate into it, eat the food, and then quickly leave. To slow the outward migration I simply cut a circle of hard plastic that fits inside the collector. I set it on top of the food used to bait the grubs into the tub. BSF grubs prefer to be under something if possible so by having the cover on top of the bait they stay in the collector much longer.
