Buckwheat flour fractions with different particle sizes (PS), comprising various concentrations of valuable nutritional components, represent an opportunity to enhance refined wheat bakery products. The aim of this research was to assess the potential of buckwheat flour (BF) fractions (large, L > 300 μm, medium, 180 μm < M < 300 μm and small, S < 180 μm) to substitute refined wheat flour at 0, 5, 10, 15, and 20% in wheat bread dough and to establish the optimal amount for each fraction. The results revealed significant changes during different bread-making stages and on the finished product. A decrease in falling number index, water absorption, starch gelatinization, elastic modulus, and bread hardness with increasing PS was observed. The increase of BF amount led to an increase in dough development time, speed of protein weakening, gel starch stability, alveograph ratio, rheofermentation properties, maximum creep-recovery compliance, and bread hardness. The optimal values for falling number, mixing–heating–cooling dough parameters, dough biaxial extension, rheofermentation, storage and loss moduli, creep-recovery compliance, loaf volume, and bread hardness were obtained depending on PS based on the generation of predictive models. It was established that the best formulations, with respect to dough rheology and bread characteristics, included BF at 9.13% for large, 10.57% for medium, and 10.25% for small PS.