Yeah I'm in the same situation, second floor flat and no outdoor area. I keep my Mobi filled up in a cupboard in our lobby area so when I get home I can grab it without tracking shit through the house first. It's the most convenient way for me.
At least I have an outdoor area and a bike stand which makes it much easier, but still need water and power. The Mobi/Jegs pressure washer would be already a big improvement over 2 buckets and a sponge, albeit it not being the dream bike cleaning porn setup of my dreams
If only I had a hose, or a power outlet for that matter..