I keep mine in a small plastic baggy ( I think the one that comes with the Bugle boy diaphragm calls ) and place it in the front pocket of what ever I'm wearing. It all depends what I have to wear for the early season.
I really like the idea of it hanging on the out side of the clothing/pockets to air dry. I'll need to find some kind of clip to hook it to my reed cow call or binos!! No roach clip here, my wife would question what I'm really doing out in the feild. Maybe a large paper clip hooked to the lanyard, great ideas guys. Thanks!