Good handwashing should be enforced at home and at daycare facilities.
Select a gentle handwashing detergent in which to soak your teddy before rinsing.
Most manufacturers suggest handwashing and air-drying to reduce the risk of your bra shrinking and/or stretching out of shape.
Use a new easy-care handwashing liquid from Ivory or Woolite.
If you don't have time to hand wash your bras and the tags say that they're machine washable, you can use a mesh lingerie bag on the gentle cycle to extend the life of the bra (though maybe not as much as handwashing would).