The use of black alder (BA) bark biomass in rigid polyurethane (PUR) foam compositions was the main task of investigation. Extractive compounds isolated from the bark through hot water extraction were used as precursors for bio-polyol synthesis via acid-free liquefaction with the polyether polyol Lupranol 3300 and through oxypropylation with propylene carbonate. The OH functionality and composition of the polyols were analyzed via wet chemistry and FTIR spectroscopy. The solid remaining after the isolation of extractive compounds was also utilized as a natural filler in PUR foams. The effects of replacing commercial polyols with bio-polyols on the foam rising rate and their mechanical properties, morphology, thermal conductivity, and thermal degradation characteristics were examined. The oxypropylated extractive-based PUR compositions demonstrated the most favorable balance between the biomass content and material properties. At an apparent density of 40 kg/m3, the compressive strength of the produced foams was enhanced by 1.4–1.5 times, while the maximum thermal degradation rate in air decreased by 3.8–6.5 times compared to reference materials without adversely affecting the foam morphology. The composition based on liquefied extractives showed lower performance but still improved properties relative to the reference foams. Introducing 3.7–14% of extracted bark into the foam compositions increased the biomass content to 22–24%, although this led to a decrease in the compressive strength and thermal stability. It was shown that partially substituting fossil-derived components with renewable bark biomass in the composition of PUR foams allows for materials with characteristics similar or better to petrochemical-based materials to be obtained. Therefore, the results presented can be considered a contribution to addressing environmental problems and promoting the development of a sustainable economy.