Answered by Shaykh Faraz Rabbani
What about hair at barbers? Re: Donating hair for wigs
It would be best to try to ask the barber to gather the hair in a bag, and to then dispose of it by burial, because the vast majority of scholars held that it is recommended to bury hair after it is separated from the body; some scholars even considered this necessary (wajib).
And Allah knows best.