The paper presents the results of a study on the effects of the addition of bread bakery waste (stale bread, sometimes infected with mold, from store returns) to agricultural waste consisting of triticale straw on the process of solid biofuel pelleting and the physical and fuel properties of the obtained pellets. The pelleting process was conducted in a pelletizer equipped with a flat matrix, with holes 6 mm in diameter, and two pelleting rollers (for straw alone and for a mixture of straw and bread waste with mass fractions of 5, 10, and 15%). The addition of bread waste during the process of pelleting resulted in reduced power demand for the pelletizer in each of the analyzed cases. The largest decrease in the power demand (by approximately 18%, i.e., from 1.27 to 1.04 kW) was recorded for a 15% addition of sunflower seed bread to the mixture with straw. Moreover, the addition of bread waste also caused a significant increase in the kinetic strength of pellets compared to pellets produced from straw alone. The highest kinetic strength was obtained in the case of pellets produced from a mixture of straw with a 15% white bread content, i.e., 99.43%. For all of the analyzed types of additives, kinetic strength increased with increasing additive content. In each of the analyzed cases, the obtained values of density of pellets produced from a mixture of straw and bread waste, as well as the kinetic strength, allow for the conclusion that the obtained pellets, in this respect, meet the requirements of ISO 17225-2:2021 and ENplus standards for Class A1 pellets.