There are sure a lot of great ideas posted. Some of them will be good to try, like the mouthwash. I did purchase 3 special hangers for my gear. After rinsing everthing in a cool water tub sometimes with and/or without a rinsing agent, the wet suit gets put on a hanger, the boots and gloves on their hanger and the BCD upside down with some air in it after draining the water on the third hanger. All of this is hung in the bathroom (due to location restraints) on a reinforced shower rod.
When we travel we make sure to hang the wetsuits and BCD's over the towel racks in the hotel room. For the boots we place these upside down on another towel rack if available.
The main thing I found for drying gear no matter what, where or how is to make sure the room it is hanging in has some sort of air flow. This may sound simple enough but some places do not have any air blowing around in the room the gear is hanging in. If this is the case leave the door open for some sort of circulation or try to drape it across the backs of chairs (or something that will not damage the gear) in an airy location. During warm weather at home I put a small fan on to keep the air moving. Otherwise as common sense would have it, the gear can get stinky.
Hope some of this helps a little bit.