Before you go getting your DSSD wet, honestly, an ounce of prevention is worth a pound of cure.
First, get two things:
Watch Gasket O-Ring Lubricator Silicone Grease
Watchmakers Silicone 7 Watch Gasket Sealer
Unscrew the crown and pull out to stop the movement. Open up the caseback with a ball of Duct Tape turning counter-clockwise. Remove the O-ring and grease it up, replace, and put your caseback on. Start slow to make sure the threads catch correctly, then tighten.
Find the O-ring on the tube, and grease that. Push your crown back down and tighten.
Both of these things are very inexpensive to purchase, and the time spent doing this will be time well spent. Any monkey can do this.
NOW you're ready to wash and use your DSSD! Dawn seems to be a popular detergent to use, with cold or slightly warm water- NOT hot. I like to wash it once with Dawn, rinse, and suds it up again using the soft brush to get into the nooks and crannies. Why? Because you want to remove as much dirt and particulates as you can before you go mushing them around with the brush.
Another idea might be to take the bracelet off and run over to your favorite non-AD jeweler to have them put it in their ultra-sonic.
Some people really prefer to use bike oil to soak their bracelets in, claiming that it gives the metal a very nice sheen. Others say that using graphite is better. The advantage of using graphite is that it doesn't attract and keep dirt. If your bracelet is supple enough, then you really don't have to do either.