You want to turn it over every so often. And adding some compost bacteria/fungi from the garden store is important since you aren't in contact with the soil, and regular compost HEAPS benefit from soil contact.
That sounds like a rather small container but will be a neat experiment. I'm thinkng you should go over to GardenWeb (another set of forums, even geekier than these, inhabited by people who take their rose bushes altogether too seriously hahaha) and check out the composting section.