I wouldn't imagine that a Barber has a lot of hair to dispose of really, where as a hairdresser would have a lot more, I would imagine that most people are just having a tidy up rather than having large volumes of hair cut off, and I would think that even large volumes of hair could be squeezed and compressed into small bin bags or bins. As I am follicularly challenged myself, (and mentally, as some would say)I cannot really give and educated answer just a guess!!
I read a really interesting article a few years ago about human hair being used in oil spills as a method of containing the spill, preventing it from forming a huge slick that floats out to sea ... I kid you not! Will have to look for a link.
I think the good hair gets passed on for wigs - my sister had her waist length untreated hair cut several years ago and they asked if they could have it for a wig.
iIlive on the edge of the New Forest and a lot of houses have problems with deer getting in their gardens and eating plants. A traditional method of stopping this is to stuff hair from the hairdressers into old tights/stockings and hand it along the boundaries of the garden - the deer think there are humans about and keep clear - honestly!
Unbeknownst to most people, manufacturers of cigarettes use bits and pieces of human hair as a "filler" in their manufacturing process. This greatly extends their supplies of tobacco and thus the cost of production.