How does chlorine bleach make a colored stain fade?

Answer: It changes the stain molecules so they absorb visible light differently

It changes the stain molecules so they absorb visible light differently ✓ — Chlorine bleach chemically changes the parts of stain molecules that absorb visible light. Its hypochlorite-based chemistry can disrupt those structures, making the color fade. This does not mean every stain molecule has been physically washed away.

It covers the colored molecules with a thin white coating — Bleach does not paint a white coating over the stain. It reacts with the colored molecules and changes their light-absorbing structure, which is also why it can fade fabric dyes.

It kills microbes whose living bodies give every stain its color — A stain does not need living microbes to have color. Tea and many dyes are colored because of their molecules’ light absorption; killing microbes alone would not remove that color. Bleach fades it by reacting with the colored molecules.