The US EPA mold site has a FAQ item about using bleach. It's the "please note" section that really stood out for me:
Should I use bleach to clean up mold?
Biocides are substances that can destroy living organisms. The use of a chemical or biocide that kills organisms such as mold (chlorine bleach, for example) is not recommended as a routine practice during mold cleanup. There may be instances, however, when professional judgment may indicate its use (for example, when immune-compromised individuals are present). In most cases, it is not possible or desirable to sterilize an area; a background level of mold spores will remain - these spores will not grow if the moisture problem has been resolved. If you choose to use disinfectants or biocides, always ventilate the area and exhaust the air to the outdoors. Never mix chlorine bleach solution with other cleaning solutions or detergents that contain ammonia because toxic fumes could be produced.
Please note: Dead mold may still cause allergic reactions in some people, so it is not enough to simply kill the mold, it must also be removed.
I'd like to save my bed but it sounds like that's risky. I wish I could treat it effectively. Beds ain't cheap.
What you can save after mold or water damage
You can easily clean and preserve materials that have a solid surface, such as plastic, glass or metal.
A mixture of 1/2 cup of bleach to 1 gallon of water is a great way to disinfect the hard surfaced materials.
Fabric clothing is easy to save by washing it in regular laundry detergent. Clean leather manually.
Larger electronics and appliances that experienced some mold exposure but weren’t under water are possible to save with cleaning.
What to throw away after mold or water damage
If an item has porous surfaces and is already moldy or was under floodwater, you will probably need to throw it away. This includes cardboard, carpet, padding, stuffed animals and upholstered furnishings. Mattresses and box springs also are on that list.
You will need to throw out most paper products, including books, once they are moldy.
For items with sentimental value, such as a wedding album, important picture or family Bible, there is an expensive but effective freeze-drying process that can preserve those items. Place the items in a freezer as soon as you can and then get them to a preservation freeze-drying contractor.
Food items that have come into contact with mold or floodwater should be thrown away.
If your home has been flooded and mold and bacteria have been left to grow for many days, it may be impossible to salvage fabric items. However, if mildew has developed due to dampness and is caught early, it can easily be removed from most fabrics.
Begin by taking the items outside to brush away as much surface mold as possible and to prevent spreading the mold spores inside your home. If the fabric is washable, use the hottest water recommended on the care label and add a disinfectant. If stains remain, create a solution of oxygen bleach and water and allow the clothes to soak for at least eight hours. Oxygen bleach can be used safely on any washable fabric.
For fabrics that are dry clean only, brush away the mildew outside and then head to a professional cleaner. Identify and point out the stains and most fabrics can be successfully restored.