Hello MaryAnn - The advantage of a compost heap is usually that it is in contact with the ground and all the critters that do the actual composting can just enter it from there. In principle there should be no reason why you can't use an old plastic dustbin. It may, however, be more tricky to get the balance right between how wet or dry the content is. You can drill or cut holes into the sides to ensure ventilation. If you look in the shops (e.g. Builder's Express) you will see that some of the commercial bins don't look much different to an upside down bin with holes in the sides (those ones are obviously in contact with the soil).
The importance of controlling the water balance in your system better is because the critters cannot escape somewhere else if things go wrong and come back later. In order to get going you could get hold of some worms (either from some friends or you can find some suppliers in the
directory and some compost activator (you might have to call a couple DIY shops to find this) or something called effective microorganism (EM), which you can also find in the directory.
As you mention, this is actually quite close to to a wormery, anyway. We have actually been experimenting with DIY wormeries for a while and are probably at system number 6 by now. You could absolutely try using your dustbin for that. There are quite a few descriptions how to build different kinds of wormeries available on the Internet and we will also be writing about our experiences on our website in the future. You could have a look what would work for you. You certainly don't need several levels or to even catch the worm tea (depending what you want to do) for a basic system that takes care of your kitchen scraps.
Any closed system will, however, need more attention and monitoring. It is somewhat like farming and the learning curve is similar.
You could certainly put your vegetable peelings straight into flower bed/pots. Just search for "trench gardening" and you should be able to find some examples of how people do this. We will also write about this on our website in the future. We
have read somewhere that similarly to adding fresh compost this may actually use some Nitrogen in the beginning while it breaks down, reducing its availability for the plants, but we have often done this for all sorts of plants and it has always worked well without any problems.
Another alternative could obviously be to ask the owners what they think about putting in a compost bin/heap permanently.
What we found is that despite this or that problem popping up along the way that it is actually very gratifying and we have certainly enjoyed the journey.
Good luck!