You mentioned that you are hanging the film to dry in your bathroom. Clean the room the day before using it for film-drying then try running some hot water for a few minutes, to get some steam in the air and drag down any remaining dust, immediately before hanging the film.

A jug style water-filter would be adequate for a source of clean washing water, although the last rinse can best be in de-mineralised water with about half the recommended amount of wetting-agent. Additionally, and obviously, check that every liquid chemical and use of water is clean of particles (perhaps by shaking them up a little then letting a spoonful dry on a dark coloured saucer, to see what is left).