The present research was undertaken to explore the influence of dried cassava bagasse (F), carboxyl methyl cellulose (CMC) and tara gum on the quality characteristics of composite wheat bread. F was used to replace wheat flour at 5 and 10% substitution levels. Dried cassava bagasse‐enriched wheat breads with CMC and CMC/tara gum binary blend (50:50 w/w) were analyzed to determine the specific volume of the breads, the crumb color, firmness and hardness. The addition of F decreased the specific volume of the breads. As the F concentration increased, the bread lightness decreased and the crumb redness, yellowness, firmness and hardness increased. The CMC was suitable for controlling the staling of the dried cassava bagasse‐enriched wheat bread. Samples containing the CMC and F at a 5% wheat flour replacement level had high acceptability by the consumers at the end of storage and resulted in higher crumb moisture content and lower crumb firmness during the storage. Practical Application Cassava bagasse (CB) is the main solid residue produced by the cassava starch industry and is made up of fibrous root material. The high moisture content prevents the use of CB by the starch industry because there is a strong possibility of microbial contamination. In this sense, drying that is simultaneous with production is essential for the effective utilization of CB. However, alternative uses for this product are necessary in order for the drying process to be economically interesting. One alternative is to use dried cassava bagasse (F) in breadmaking. The addition of F to bread has not been investigated. Hence, more studies are necessary for a better understanding of the effect of a partial substitution of wheat with F to obtain fiber‐wheat composite bread. Moreover, it is also necessary to increase dietary fiber intake, taking into account the fact that customers demand healthier foods.