Having now done some pottery I understand the difference between the bucket for reclaiming your earth clays and the polymer clay version. Last year or the year before I broke down and set up plastic shoeboxes for my scraps. I do a lot of claying and it still took me years of one bucket or, more recently, one bucket and a few gallon zipper bags, before I got to this stage. I dutifully labeled my boxes with the colour groups I work with and started sorting my big bucket into them. All new scraps and cane ends got dumped in.
This summer I have a little help in the studio and my help volunteered to process the scraps. We saved the better cane bits because the students love those but all of the rest of the colours got divided into 5 or 10 groups per colour and mixed until they became colours. We ended up with dozens of sheets of clay, in dozens of colours, and weighing in around 15 pounds of new-to-me clay.
From the new clay we did a kids event, the canes for some fairy houses, and the houses themselves. The inside of the houses are pre-baked blobs of very muddy scrap clay.
How did we store the end products? In blocks back in the boxes, separated by bits of wax paper.