Agree with Latt's suggestions.
If you have a 5 gal bucket just put your seng in there and fill over it with water and let it soak a while (30 minutes or hour will work).
That will losen up any dried or stuck on dirt.
Then just pour that off and can use a hose sprayer (not too much force) to remove remaining dirt.
Dont worry about getting them spotless, a little dirt remaining in the stress rings and crevices sort of enhances the color once dry.
I usually just shake the excess water off mine and then let it sit on a towell for a hour or two to air dry a bit then move it to a window screen that I have setup in a small room with air/vent. Spread it out thin so it's not piled on top of other roots.
I just dry mine at normal inside air temp (72-74 degrees) and it takes 4-6 weeks to completely dry larger diameter roots.
Historically seng prices usually reach their peak around Thanksgiving or just before Christmas - so there is no real need to rush up the drying process (unless say you are strapped for cash).
If you needed to speed that up for some reason, you could purchase one of those little fan/forced air heaters at Walmart (with a thermostat) and set it for like 80-85 degrees and let it blow that warmer/dry air in and around your window screen area. That would probably cut your drying time by 1/2 or 1/3.
Don't try to dry it too fast, or expose to excessive heat (say over 90-95 degrees) or to direct sunlight. That can damange the roots, change color, carmalize the inside and seriously reduce the market value.
Good Luck !