Strip the entire bed of sheets, dust ruffle, pillows, mattress covers and blankets. Launder these items according to the labels with bleach-free detergent.
Set up a fan close to the bed to keep air circulating and open any windows and doors in the room.
Fill an empty spray bottle with hydrogen peroxide and replace the cap.
Spray a thin mist of hydrogen peroxide over the entire mattress if you do not know where the bleach smell is coming from, or only in the spot where bleach has been applied to the surface if you do know where the problem area is.
Check the mattress for the smell of bleach. If it remains, blot the peroxide away with a towel and spray a new layer. Repeat this until the bleach is no longer detectable. Blot with a towel each time to avoid over-saturating the mattress. Allow the mattress to dry completely, which may take 24 hours.
Replace the bedding.