Taking this straight from a site
Chitosan textile production
Traditionally, chitosan is mainly treated on a yarn’s or fabric’s surface [2, 3, 4, 5, 6] and is exposed to harm from abrasion and other movements. Chitosan peals when it wears, and the biofunctions are vulnerable to physical and chemical damage. Producing a pure fibre from chitosan is a reasonable means of improving stability and durability.
Chitosan fibres are derived mainly from wet spinning. Dissolution, deaeration and filtration of chitosan are performed before spinning . The semi-finished fibres are then refined, dried and post-finished. Factors in dissolution, deaeration and drying are vital to control properties of chitosan fibre, including solvent, pH and concentration during dissolution, method and agent of drying, etc. A study  shows that methanol drying yielded chitosan fibre has superior mechanical properties to fibres dried using other methods and agent.
The three main methods are available for producing a fabric from fibres. A nonwoven method entails entangling fibres by using water or air jets. This process is similar to wool felting and requires no yarn spinning. The nonwoven method is fast and cheap, and it is suitable for producing cheap, disposable products. Woven and knit fabrics are more durable and are more suitable for daily use because they can be reused hundreds of times, withstanding frequent washing and abrasion
While not strictly insectile chitin, the thing that bee fuzz is made of, I think it is similar enough to apply due to the high amount of mentions of chitin-chitosan in the doc