For me, I use a very old toothbrush and toothpaste. Of course I remove the bracelet from the watch. After that is done, wash with soapy water and another round with the tooth brush. Finish off with a soak in warm water and dish washing fluid. I also swirl or jiggle the bracelet in this mix a few times. I let it soak until the water is cool and final wash in running water.
If really dirty, then have a go with a tooth pick to loosen any grime and DNA. If really really bad, then a visit to my watch guy and have a go at his ultrasonic cleaner.