The desire to whiten fabrics is time-honoured and, for much of the world, exposure to strong midday sunlight is the natural and cost-free way to achieve this. Where cotton is milled and prepared for printing, metres upon metres need to be daily bleached, an important factor in explaining where the industry has mostly developed, i.e. close to the equator such as throughout India and southern USA.
In the past every household or housemaid hung the linen out to bleach in the sun, perhaps a time luxury today and not strictly necessary but, hanging bedding especially out in the midday sun in the hottest months, even a couple of times a year, keep them fresh and white, and the lovely summery fresh smell is not to be missed.
Potash and lye baths have also been used for millenia as bleaching solutions for both textiles and timber. Lye–caustic soda–can be used (with care) for home bleaching, especially oak tables, and to re-whiten. In 1785, chlorine was discovered to be a powerful bleaching agent, and since then many more chemical methods have been marketed.
Snow is another well known natural bleaching agent, that really is worth making use of.
Snow Country Yasunari Kawabata Penguin classic 2011