I'm not sure about the waterlogged soil in the bucket. I would have thought that any aerobic processes which would normally keep the 'soil' healthy have stopped with all the water. Whether the contents in the bucket is useless now, is another matter. Water meadows flourish with new growth when they're not flooded so perhaps using the soil wouldn't be too problematic. I would suggest you might want to add in some fresh stuff to it. Hopefully, someone who knows more about soil biology will be along with a more scientific answer.
In the long term, have you considered something like a mini hot composter? It wouldn't take up much more space than your bucket and has the advantage of composting kitchen scraps too.
Something like this
HOTBIN Mini (100ltr)
It has a footprint of just 45cm x 45cm so wouldn't take up too much space. I know they say there's an art in getting the right balance of stuff to add to get great compost out but I add spent soil to mine along with shredded confidential papers, kitchen scraps, lawn clippings and weeds and it seems to produce compost without too many problems. It doesn't produce loads but it sounds as though you don't need a huge amount.
ETA: Sort of what
cesare was suggesting.