I like to use a bit of the car wash with wax as it aids drying quite a bit.
To dry, I simply put the separated wet brass on a dedicated and full size bath towel. Fold lengthwise to make a long burrito (as mentioned previously).
Then grab each of the longs ends and alternate tipping ends to tumble the brass inside the towel. Be aggressive and the brass will be 90% dry in just a half dozen tumbles.
Then I place it on the same towel and put a mini fan across it. Dries quickly enough to be spotless either in the morning or in the afternoon when I get home from work.