Once the fruit flies have found the bin, they are almost impossible to get rid of. I would imagine that an outdoor bin will always be susceptible. If you are not adverse to spraying, Hot Shot kitchen bug killer (available at Walmart) will kill the flies without harming your worms.

I've had infestations in my studio apartment and gotten rid of them.

1. Set up a trap with a small hole they can get in but often can't find to get out, some water with something to attract them (I put in a bit of rotten fruit and put saran wrap over it with a small hole.) They smell the fruit and can find the hole to get in but then can't get out. Put it near your bin.

2. Freeze all your produce before putting it in. FF eggs are often in the rind when you get them from the store. (It speeds up degradation for the worms anyway and if you're doing it for the FF eggs you don't have to feel guilty about using more electricity just to make the worms happier ;-)

3. Put a tall layer of bedding on top of the working food layer. I was told and it seems correct to me that FF won't burrow down in to something to lay their eggs. They'll only lay the eggs if the food is on the surface.

I don't cover my bin - the worms need oxygen. I just have about 8 inches of machine shredded crinkled up newspaper (actually phone book). When this paper gets wet and turns in to actual moist bedding with food on top of it, it's less than a quarter inch thick, so it's not really all that much paper, but dry with air pockets it's bulky and prevents both fruit flies and fungus gnats.

It will take quite a while, but it can be done. Good luck!!!

Oh yeah this is a battle you're going to have to fight for a little while before they're gone. But also know that they'll come back some day. So what ever you find to work for you, write it down and start fighting as soon as you see the first little bugger.
First, for now, any produce you have to eat for yourself, keep in the fridge so they can't go after that when the bin becomes someplace they don't want to be.
And luckily I think where you are it's going to get cold enough soon enough for them to die off naturally until spring anyway. So your battle may be short for now.
The only way I was able to kill all of mine off was to stop feeding for a month, let the bin dry up to a fluffy stage and keep a flying pest strip on top top of the bin. It's a white hard plastic thing with a yellowish solid thing inside it. It gives off fumes that kills anything that flies. Moths, flies, gnats, fruit flies, etc. I just set that on top of my flow through and swept up the dead ones from the floor. It took some time, but it worked.
I always buried the food well and there was always plenty of bedding on top of everything but the little buggers found their way in some how. Since yours is a cooler though, it may help, so give it a try as well.
Good luck. Don't give up.

Fruit flies are a bit easier to get rid of than fungas gnats.

Once the food is gone, so will the fruit flies. If there's no food, they'll disappear.
As mentioned, freeze all of your food first.

Fungas gnats are harder. They love dark, moist soil. Fungas gnats are often found around houseplants in the winter, because people tend to overwater their plants and don't take in consideration the lack of sunlight.

So for this reason, fungas gnats love our bins.

You can get a little jar and put some cider vinegar with a drop of dishwashing liquid in. The flies will be attracted to the smell and the dishwashing liquid prevents them from getting out.

Always cover your food with lots of shredded paper. Flies won't dig to get at the food. If it's out in the open, easily accessible, they'll swarm to it.

Open the door to the balcony only wide enough to stick your arm through to open the cooler, then quick close the door. In 5 minutes the fruit flys should be gone and it will be save to go out.

I have 5 bins, and definitely DO NOT have a permanent fruit fly infestation.

Freeze the food scraps before you put them in to destroy any eggs fruit flies might have laid on them. When you put food in the bin, bury it.

Those 2 things should take care of your fruit fly problem.

Deanna