The results of comprehensive studies on accelerated (artificial) ageing and biodegradation of polymer biocomposites on PBS matrix filled with raw wheat bran (WB) are presented in this paper. These polymer biocomposites are intended for the manufacture of goods, in particular disposable packaging and disposable utensils, which decompose naturally under the influence of biological agents. The effects of wheat bran content within the range of 10–50 wt.% and extruder screw speed of 50–200 min−1 during the production of biocomposite pellets on the resistance of the products to physical, chemical, and biological factors were evaluated. The research included the determination of the effect of artificial ageing on the changes of structural and thermal properties by infrared spectra (FTIR), differential scanning calorimetry (DSC), and thermogravimetric analysis (TG). They showed structural changes—disruption of chains within the ester bond, which occurred in the composition with 50% bran content as early as after 250 h of accelerated ageing. An increase in the degree of crystallinity with ageing was also found to be as high as 48% in the composition with 10% bran content. The temperature taken at the beginning of weight loss of the compositions studied was also lowered, even by 30 °C at the highest bran content. The changes of mechanical properties of biocomposite samples were also investigated. These include: hardness, surface roughness, transverse shrinkage, weight loss, and optical properties: colour and gloss. The ageing hardness of the biocomposite increased by up to 12%, and the surface roughness (Ra) increased by as much as 2.4 µm at the highest bran content. It was also found that ageing causes significant colour changes of the biocomposition (ΔE = 7.8 already at 10% bran content), and that the ageing-induced weight loss of the biocomposition of 0.31–0.59% is lower than that of the samples produced from PBS alone (1.06%). On the other hand, the transverse shrinkage of moldings as a result of ageing turned out to be relatively small, at 0.05%–0.35%. The chemical resistance of biocomposites to NaOH and HCl as well as absorption of polar and non-polar liquids (oil and water) were also determined. Biodegradation studies were carried out under controlled conditions in compost and weight loss of the tested compositions was determined. The weight of samples made from PBS alone after 70 days of composting decreased only by 4.5%, while the biocomposition with 10% bran content decreased by 15.1%, and with 50% bran, by as much as 68.3%. The measurements carried out showed a significant influence of the content of the applied lignocellulosic fillers (LCF) in the form of raw wheat bran (WB) on the examined properties of the biocompositions and the course of their artificial ageing and biodegradation. Within the range under study, the screw speed of the extruder during the production of biocomposite pellets did not show any significant influence on most of the studied properties of the injection mouldings produced from it.