Bread residues represent a significant fraction of retail food wastes, becoming a severe environmental challenge and an economic loss for the food sector. They are, however, an attractive resource for bioconversion into value-added products. In this study, the edible filamentous fungi Neurospora intermedia and Aspergillus oryzae were employed for the production of bioethanol and high-protein biomass by cultivation on enzymatically liquefied bread-waste medium at 150 g/L solids. The fermentation of hydrolysate by N. intermedia resulted in the ethanol titer of 32.2 g/L and biomass yield of 19.2 g/L with ca. 45% protein. However, the fermentation ended with a considerable amount of residual fermentable sugars; therefore, the liquid medium after the first fermentation was distilled and fermented again by two fungal strains (N. intermedia and A. oryzae). The fermentations resulted in the production of additional ethanol and biomass. A. oryzae showed better performance in the production of biomass, while the other strain yielded more ethanol. The final products’ yield ranged 0.29–0.32 g EtOH/g and 0.20–0.22 g biomass/g bread waste depending on the strain used in the second fermentation. The study shows that valorization of bread residuals by fungi is a promising option for the production of biofuels and foodstuff within the circular bioeconomy approach.