In this study, anionic dialdehyde cellulose (DAC) and cationic dialdehyde cellulose (c-DAC) nanofibrous adsorbents were prepared via a two-step reaction from bamboo pulp, using sodium periodate and Girard’s reagent T as oxidizing and cationizing agents, respectively. The performance of DAC and c-DAC for selective dye adsorption and separation was evaluated by six different organic dyes (with varying charge properties) and certain binary mixtures. Both adsorbents could remove the dyes but with different capability, where DAC exhibited high adsorption efficiency against cationic dyes (e.g., the maximum adsorption capacity for Bismarck brown Y was 552.1 mg/g) and c-DAC exhibited high adsorption efficiency against anionic dyes (e.g., the maximum adsorption capacity for Congo red was 540.3 mg/g). To investigate the adsorption mechanism for these adsorbents, effects of contact time, initial pH value, initial dye concentration, and ionic strength on the adsorption activity against Congo red were investigated. The adsorption equilibrium data of DAC were found to fit best with the Langmuir isotherm model, whereas that of c-DAC were found to fit best with the Freundlich model. Both DAC and c-DAC adsorption kinetic data could be described by the pseudo-second-order kinetic model, and these adsorbents possessed stable adsorption efficiency in the pH range of 4–10. Furthermore, their dye adsorption capabilities were found to increase with increasing ionic strength (salt concentration). The distinctive complementary features of DAC and c-DAC will allow them to remove a wide range of organic dyes from industrial wastewater.