I shake the cases around in a scrap terrycloth towel, set it on a flat surface and tap each case head against the towel to knock out any water held in the flash hole. I then lay them on some fresh towel and forget about them for three days. They are then dry.
And, if I'm in a hurry (or part of the basement with minimal air flow), I'll turn a box fan on to get some air moving.
Before I go to bed, I stir the cases a bit and turn the fan off.
With a fan, they're usually dry in less than 24 hours.