A balanced diet, rich in fruits and vegetables and ensuring the intake of natural products, has been shown to reduce or prevent the occurrence of many chronic diseases. However, the choice to consume large quantities of fruits and vegetables leads to an increase in the amount of waste, which can cause an alteration in environmental sustainability. To date, the concept of a “byproduct” has evolved, now being understood as a waste product from which it is still possible obtain useful compounds. Byproducts in the agricultural sector are a rich source of bioactive compounds, capable of possessing a second life, decreasing the amount of waste products, the disposal costs, and environmental pollution. A promising and well-known citrus of the Mediterranean diet is the bergamot (Citrus bergamia, Risso et Poiteau). The composition of bergamot is known, and the rich presence of phenolic compounds and essential oils has justified the countless beneficial properties found, including anti-inflammatory, antioxidant, anti-cholesterolemic, and protective activity for the immune system, heart failure, and coronary heart diseases. The industrial processing of bergamot fruits leads to the formation of bergamot juice and bergamot oil. The solid residues, referred to as “pastazzo”, are normally used as feed for livestock or pectin production. The fiber of bergamot (BF) can be obtained from pastazzo and could exert an interesting effect thanks to its content of polyphenols. The aims of this work were twofold: (a) to have more information (composition, polyphenol and flavonoid content, antioxidant activity, etc.) on BF powder and (b) to verify the effects of BF on an in vitro model of neurotoxicity induced by treatment with amyloid beta protein (Aβ). In particular, a study of cell lines was carried out on both neurons and oligodendrocytes, to measure the involvement of the glia and compare it with that of the neurons. The results obtained showed that BF powder contains polyphenols and flavonoids and that it is able to exercise an antioxidant property. Moreover, BF exerts a protective action on the damage induced by treatment with Aβ, and this defense is found in experiments on the cell viability, on the accumulation of reactive oxygen species, on the involvement of the expression of caspase-3, and on necrotic or apoptotic death. In all these results, oligodendrocytes were always more sensitive and fragile than neurons. Further experiments are needed, and if this trend is confirmed, BF could be used in AD; at the same time, it could help to avoid the accumulation of waste products.