Lots of 'washing' hands (both with just soap and water as well as alcohol infused wipes), wear light colored clothing (white preferably) and make sure your Pasta Machine is squeeky-clean. I've decided a while ago that having a (slightly dusty) ceiling fan going close to my workspace probably does not help in keeping white clay white and neither do the heating/cooling registers that are above my work space. You may want to check those things. Other than that, white clay is just difficult to keep white. Depending on what you are making, sometimes the white clay can be 'cleaned up' if you wipe it lightly with alcohol, although if the 'dirt' and fuzzies are embedded, even the wiping will not do you any good.
People go to great lengths for this. Some sculptors even have white lint free outfits they wear while working with the clay. There is a whole section on tips for this at www.glassattic.com. ( under sculpture)
Info below is from the "magic archive", so I don't know if there's anything there that might prove helpful. Hope so. Links are often to just one particular post, but often reading the entire thread can be helpful.