Most of us are familiar with household (chlorine-based) bleach, which is sodium hypochlorite. It is a very powerful bleaching agent and, like similar agents used in the industrial bleaching of fabrics, it has by-products that include; dioxins, furans and organochlorides.
An alternative to a chlorine based bleach is Hydrogen Peroxide (H2O2). This has medical uses and domestic uses such as for bleaching hair.
Hydrogen peroxide occurs naturally by the action of sunlight on water and is simply water plus an extra oxygen molecule (2 lots of H20 plus one lot of 02 equals 2 lots of H2o2 for all you chemists). Hydrogen peroxide is quite reactive and so easily gives up some of its oxygen to revert back to water. This act of giving up oxygen to something else, like fabric, causes the fabric or impurities in it to be oxidised. The oxidised parts of the fabric are chemically changed and lose their colour. They remain there but their colour is changed. That’s what makes it a bleach and so the end products are just the oxidised fabric and water.
Natural linen has a light brown or beige colour. To go lighter than this it has to be either bleached, or bleached and dyed.
If your clients are environmentally conscious and concerned about the environmental impact of the products they buy from you, it would be prudent to ensure that your linen is hydrogen peroxide bleached rather than chlorine bleached.