The two bucket method is good. But as lextech said, you need to get rid of the chamois (or just save it for the glass), and get some microfibre drying towels, which will minimise swirl mark creation. You can just drape them over the wet area and pull them towards you, no need to rub them dry. Check out some examples of the kind of thing I mean here. I recommend you get at least two, one for the upper parts of the car, and one for the lower.