In an eco-friendly context, an adsorption study was performed in a fixed-bed column system to remove organic pollutants from dyeing wastewater, testing preliminary theoretical models and reactive blue 5G (RB5G) dye as a reference pollutant and tilapia bone-based biochar as an alternative adsorbent. Adsorption approaches in removing RB5G dye molecules from synthetic solutions were performed to understand better based on a reliable mathematical representation and provide insights and strategies into treating dyeing wastewater. Initial dye concentration, pH, temperature, and stirring velocity were used as process variables to search for maximal capacity in batch mode. Thermodynamic analysis and a series of phenomenological kinetic models were applied to understand and interpret the mechanisms and develop a predictive model for a fixed-bed column adsorption system, trying to minimize the total organic carbon (TOC) in dyeing wastewater. An intraparticle mass transfer resistance model and the Langmuir-BET isotherm better represented kinetic and equilibrium data, respectively. In the Langmuir-BET model context, the first monolayer has systematically changed its predicted Langmuir adsorption capacity from 18 mg g-1 to 31 mg g-1 being favored by the increase in temperature of 30 to 60 degrees C, respectively, with the lowest Gibbs free energies for the multilayer formation ruled by weak physical interaction. Theoretical values of the breakpoint, full saturation time, and useful column height were well predicted related to their experimental ones, including the better fitting of all adsorption curve patterns in a fixed-bed adsorption column system with an adsorption capacity of 30.4 mg g-1 (at 50 degrees C) for an inlet of 200 mg L-1 RB5G solution resembling almost the same value found in batch mode (30.9 mg g-1). After treating the dyeing wastewater characterized by 75 mg L-1 RB5G dye, the adsorption capacity of 23.3 mg g-1 was attained with a 12% loss in comparison with the expected one for a synthetic RB5G solution due to adsorptive competition with other organic pollutants. Finally, a final TOC value near 5.0 mg L-1, the maximum allowed for the Brazilian environmental council, was attained with an almost zero RB5G concentration after a 5-h breakpoint.