The use of residual microbial biomass from various industries in emerging pollutant removal strategies represents a new area of research in the field. In this case, we examined how to remove reactive dyes from an aqueous solution utilizing a biosorbent made of residual biomass from immobilized Saccharomyces pastorianus (S. pastorianus) in a polymer matrix using a dynamic system. Fluidized bed column biosorption investigations were carried out on a laboratory scale. Brilliant Red HE-3B was chosen as the target molecule. The main parameters considered for this purpose were the flow rate (4.0 mL/min; 6.1 mL/min), initial pollutant concentration (51.2 mg/L; 77.84 mg/L), and biosorbent mass (16 g; 20 g). The experimental data of the fluidized bed study were evaluated by mathematical modeling. The Yoon–Nelson, Bohart–Adams, Clark, and Yan models were investigated for an appropriate correlation with the experimental data. An acceptable fit was obtained for a flow rate of 4 mL/min, an initial pollutant concentration of 51.2 mg/L, and a biosorbent amount of 20 g. The obtained results indicate that the biosorbent can be used efficiently in a dynamic system both for the removal of the studied dye and in extended operations with a continuous flow of wastewater. As a conclusion, the investigated biocomposite material can be considered a viable biosorbent for testing in the removal of reactive dyes from aqueous environments and creates the necessary conditions for the extension of studies toward the application of these types of biosorbents in the treatment of industrial effluents loaded with organic dyes.