Dye wastewater containing bisphenol A (BPA) and dyes as pollutants have not been adequately studied. Our previous study revealed that thermoplastic polyurethane (TPU) nanofiber membranes (NFMs) modified by the addition of polyethyleneimine (PEI) and polydopamine (PDA) satisfactorily adsorb dyes. Herein, we first optimized the synthesis conditions for such membranes, noting a PEI:PDA monomer ratio of 2:2 and a deposition time of 48 h to be optimal. Experiments using these membranes revealed that binary systems containing BPA and the dyes (Congo red (CR), Eosin yellow (EY), or sunset yellow (SY)) exhibit three adsorption behaviors. CR and BPA compete with each other for adsorption sites, decreasing the maximum adsorption capacity (Qmax) for CR 208.3 mg/g (in a monomeric system) to 182.4 mg/g, whereas for BPA, it decreased from 26.7 to 22.8 mg/g. The adsorption rates for CR and BPA decreased from 0.002 min−1 and 0.331 min−1 in the monomeric systems to 8.37 × 10−4 min−1 and 0.072 min−1, respectively, in the binary CR–BPA system, exhibiting antagonistic effects. When EY and BPA coexist, Qmax for EY increased from 60.0 (monomeric) to 71.9 mg/g, whereas that for BPA increased from 35.6 to 43.2 mg/g, showing a synergistic effect due to the possible bridging effect. The adsorption sites for SY and BPA are independent of each other. Thus, PDA/PEI TPU NFMs exhibit the potential for removal of dye–BPA composites, whereas binary systems containing BPA with different dyes are adsorbed differently.