I toss them in my dehydrator. Run it at 150 until I remember they are in there 
As for the dust thing, add dryer sheets to your media but also if you are getting that much residue on your brass you need to change out your media.
It's brand new media.
I did the dryer sheet on the last batch, last year, but forgot to throw it in this past weekend on the latest batch. It's not a ton of dust. When I pull them out I tape two cases together upsidedown to knock out the media and wipe the outside with a paper towel; after 100 rounds the paper towel is a little discolored with the dust wipe off. Looking inside you can tell the case walls have a little dust and are the color of the media dust not shiney brass looking like the outside. I plan to just run a qtip with a little case lube on the inside of the neck, to clean the dust and outside to lube the neck for neck sizing only and call it good.
Walnut media makes a lot of dust (especially that red Lyman stuff), but corncob doesn't. If you cut up strips of paper towel and leave them in the walnut media it helps a lot, but you'll always have some dust.
For drying, I just dump the brass on a pizza pan in the oven at 200* for a while.
