Bleaching with Hydrogen per oxide (H2O2):

Hydrogen peroxide (H2O2) is a simplest peroxide (compound with oxygen-oxygen single bond). The pure hydrogen peroxide is a colourless liquid, slightly viscous than water. It is strong oxidizing agent and used as a bleaching agent and disinfectant. It was first used as bleaching agent in 1920's. Today, it is estimated that 90 to 95% of cotton and cotton/synthetic blends are bleached with hydrogen peroxide. For commercial use the the hydrogen peroxide is available 35 to 70% concentration. It is ecologically acceptable and economically feasible.  

Mechanism of Hydrogen per Oxide:

Hydrogen peroxide is weak acid and in water it is ionize to form a hydrogen ion and a perhydroxyl  ion   as per the given equation:

H2O2  +  H2O----------------H+         +       HOO- (Perhydroxyl ion) 

This perhydroxy ion is the active hydrogen peroxide and unstable and break down as per the following equation: 

HOO(-) ---------------  OH(-)    +   O (Active and Nascent oxygen)

The bleaching, most probably takes place via the reaction of HOO(-) or O with coloured material (Like grey cotton) where by they oxidized into colourless compounds. 

Since the amount of HOO(-) at pH 7 is extremely small, neutral solutions of hydrogen peroxide are quite stable.The catalytic effect of transition metal ions (e.g. Cu++, Fe+++) on hydrogen peroxide, accelerating its decomposition and may cause great damage to the fibre.

In order to activate hydrogen peroxide for the bleaching reaction to take place, a base is added to the bleaching bath. The base will shift the equilibrium dissociation to the right:

NaOH    +   H2O2 ----Equilibrium-----------------Na (+)      +   HOO (-)   + H2O