How long does it take for human hair to decompose?

Hair on mummies may be preserved for thousands of years.
https://www.quora.com/What-is-the-decay-decomposition-rate-of-human-hair

Mummification is fairly unusual, though, occurring only when conditions are very dry.

The rate of decomposition depends on the volume of hair, temperature and humidity, and the presence of keratin-eating bacteria (keratin is the fibrous protein forming the main structural constituent of hair, fingernails, feathers, hooves, horns, etc.) and certain insects.

On average the process takes about a year.

https://en.wikipedia.org/wiki/Forensic_entomological_decomposition

The hair of the Tollund Man was fairly well preserved for 2000 years - as was his body.

https://en.wikipedia.org/wiki/Tollund_man