You have got it right. I usually replace the coffee filters each run.
After I run it through, I do it once more, then ditch the rinsed material into a trash bag, along with the filters, then new filters, and new bone dry, material.
After I run it through, I do it once more, then ditch the rinsed material into a trash bag, along with the filters, then new filters, and new bone dry, material.