GreenGardener12, I think the Urban Composter product you were looking at uses the Bukashi system, except the bacteria in the system you have looked at are supplied in a spray rather than in a bran, which is what I use.
I have a small-ish city garden - big enough for some compost bins though, so sounds bigger than yours. No lawn, so all my compost is from kitchen waste and any dead plant material I gather in the garden. I never have enough compost so was keen to try the Bukashi system. You can add all sorts to this - including cooked food, bread, meat and fish, none of which can go on a compost heap, as well as the tired fruit, veg peelings, teabags etc which I usually put in my compost bin. You fill up the bin, adding Bukashi bran (or the spray in the system you have looked at) to each layer of food as it goes in. Then once the bin is full, leave it sealed for a couple of weeks while it "cooks". I have two bins, so I can start filling a second whilst the first one is cooking.
You might get a very strong liquid from the tap at the bottom of the bin, depending on how wet the waste you put in is. This is VERY strong and has to be diluted 1:100 with water. I generally only get about two teaspoons worth (after tipping the bin so any liquid comes out through the tap), so collect it in an old litre milk bottle and top it up with water. Plants love it. After about a fortnight, if there is a kind of white mould on the material in the top of the bin - which will smell quite strongly of vinegar - it's ready for the garden. However it doesn't break down to compost-like material in the bin - it is just kind of pickled? (There are useful videos on this subject on You Tube, made by Bukashi fans!).
At this stage, I empty the bin into my compost bin and cover it with a layer of other material, but you can also dig it into soil, so this might be ideal for your borders. You'd need to dig down a few inches, bury it and cover it with about 6" of soil. I have found it breaks down really quickly in my compost bin, much faster than the other material I put in there, and it makes the whole compost bin break down quicker. Eventually it breaks down to a rich humus, alive with worms.
As you haven't space for a compost bin, this might be something to think about? Another idea is to dig a deep hole in your border and just fill that up with the stuff you would normally put in a compost bin. A friend of mine with a small garden does just that. It will break down slowly and you can either dig up the compost after a while or start another hole somewhere else - the worms will fertilise your borders for you! If you have a lot of grass clippings, make sure you mix in plenty of brown material, such as paper, cardboard or dead leaves, otherwise it will just go slimy and not rot well.
An Urban Composter starter kit will probably set you back about £45, and they do take up a bit of space. Ideally, you should keep them in/near your kitchen, where the waste material is produced. If you go for the spray option, at least you won't have to worry about finding space for a 1kg bag of bran as well, but it might be a less economical option. I am really impressed by the results and I get a nice warm feeling knowing that I am putting waste to good use in my garden!
Let us know how you get on!