I was looking at another site and saw someone asked a question about how long it takes for cotton clothes to decompose in a landfill.
The main answers were all saying the same thing, that nothing decomposes fast if at all in a landfill because of the lack of oxygen, so cotton will probably take 20-200 years.
Apart from that I loved this answer so much I wanted to share it here:
Landfill conditions are notoriously anaerobic, so ANYTHING in a landfill will not decompose barely at all. It may take 20-200 years. Fact is, few things decompose in landfills, organic waste anaerobically decomposes producing some methane and not much else.
It's much better to reuse cotton as rags. I use old t-shirts as cleaning rags, then when no longer any good, I wash em one final time then recycle cotton. Better long term strategy is that cotton can be shredded and composted to feed mushrooms. Indoor cultivation of Volvariella volvacea otherwise known as Straw Mushrooms which are edible.
There are a lot of things that I might have thought of to do with an old shirt, but I never ever thought about using it to grow mushrooms!