Rubbermaid bins are made from low density polyethylene. There is no glue that will hold effectively to polyethylene. When you need to join polyethylene parts, you weld them together. Polyethylene sweats oil, which will eventually cause any glued joint to fail.

The best way to prevent fruit flies and fungus gnats is to freeze everything that is placed in the bin that has any possibility of carrying fruit fly eggs.

Thanks for the tip on freezing. I've read that somewhere else before.
Since this will be my first attempt, I'm trying to make sure that things will be as tidy as possible.
Are there similarly suitable containers, made of different material, that WOULD allow for attaching screen?
Thanks for the help. This forum is great!!!

You could put a 'vent' through the wall of the plastic then screen the vent. Some vents come in two parts so you just screw the two parts back together with something like nylon tights between them. Bentley has something like that on redwormcomposting.com.

Reiki, I would not bother with screening the vent holes at all. Make the holes plentiful but small to prevent escapes. I am also trying to keep my worm hobby as neat and tidy as possible. The pot worms seem to stay in place, there are few fruit flies as I limit the fresh fruit fed. I vaccuum the area around the worms regularly just in case I spill something when I go to feed. I keep my bins in a tray to also help. So far I have seen no discoloration in the carpet or signs of a problem. Instead of trying to keep a landlord happy I have to keep a wife happy.

Freezing is one thing that will help, but will not totally resolve the fly problem. To really prevent flies, you should really have full control over all the air flow in your bin.

Here is a link of my modified COW which totally prevent flies. I was frozing my waste before and also putting some news paper on it or vermicompost, but since 1 year i use a simple way, i do not frozze nothing and put directly every day my waste on the top without anything on it, and the result: NO FLY. This is not recommended, your worm bin has really to 100% control the air flow otherwise fly infestation will be on you soon.

In my case i've put some special material (that let air pass through) on air trap with duck tape. I also put some duck tape around some layer, since there was 1 or 2 mm where fly could pass. Fly can pass through a 1mm hole, keep this in mind.

Here is a link that might be useful: Lombricompostage.org - Forum post

I'm one who attempted to glue screen to her plastic bins and had it fall off after a couple months. I've moved to a system where I place a large piece of fabric on top of everything before and after each feeding. It definitely allows for air flow and does at least as good of a job of screening pests as metal mesh would. When it starts to look mucky, I just bury it and start with a new one. But I'm a quilter, so I have lots of fabric scraps.