Is the goal sheets made from a breathable fabric?
The thread count and tightness of weave may also need to be considered.
One overview on fabrics and their usefulness for bedding.
Raw bamboo linen fibre requires a long and expensive process to extract, compared to products such as natural linen from flax.
As @phb pointed out the majority of woven materials sold as ‘made from bamboo’ are not really the natural fibres found in the bamboo. They are reconstituted cellulose polymers. The bamboo or indeed any cellulose based plant can be chemically dissolved to release raw cellulose. Threads such as rayon etc are produced from the extracted plant cellulose. Rayon could equally have been man made from a gum tree, a pine tree or even a rose bush.
Cellulose is also the principle polymer used in the manufacture of paper.
If I had the inclination I could process rose bush cuttings to produce rose rayon. The product could be sold as rose tee shirts and rose bed sheets for that perfect nights comfort, soft as a rose petal. 100% natural in the same way all cellulose based synthetic fibres are.
There are natural fibres that are readily available and directly processed. EG wool, silk, cotton, coir (coconut fibre).
Other natural fibres are obtained by physically (mechanically) breaking down the plant. This extracts the natural fibres hidden within the plant without substantial alteration of their form in the plant. EG flax and hemp.
The use of living plants with fibrous structures to make other products has long been established. Papyrus for paper, jungle vines for ropes and canes for weaving, paper from mulberry tree bark.
Raw Bamboo can also be mechanically broken down and processed to release the fibre content within the plant walls. It’s not as simple as other plants which is why early paper making in China used silk, mulberry bark, hemp etc for creating writing materials. The bamboo process is expensive and time consuming. It produces a glass like fibre which is very strong.