Monitoring endocrine-disrupting chemicals such as bisphenol-A (BPA) is of great concern because its exposure may lead to reproductive problems, neurotoxicity, mutagenicity, and even carcinogenicity. Herein, we reported the fabrication of an efficient electrochemical sensor based on CuO–NiO wrapped cellulose acetate/polyaniline electrospun nanofibers at a Ni foam (CuO–NiO/CA–PANI@NF) electrode for the sensitive and selective monitoring of BPA. CA–PANI-based electrospun nanofibers were selected because of their improved electrical conductivity and charge density, high binding affinity toward BPA via alternative amine and imine groups, and low cost, thus paving the way for the smooth and uniform flow of ions. However, CuO–NiO-based nanoparticles offer more exposed catalytic active species such as NiOOH/CuOOH for the fast electrocatalytic oxidation of BPA. Thus, the synergistic effect of CuO–NiO nanoparticles with electrospun nanofibers leads to high sensitivity (0.00172 μA/nM/cm2) with a low limit of detection (0.6 nM), a wide linear range (2–100 nM), and high selectivity, even in the presence of interferences, including Co2+, Cd2+, Na+ Pb2+, Ni2+, Cd2+, Ca2+, Fe3+, NO3 2–, SO4 2–, Cr6+, Br–, Mg2+, Zn2+, and Ba2+ and molecules such as bisphenol-B, bisphenol-F, and phenol. The designed electrode was successfully applied to monitor BPA from plastic bottled water with high precision, thus suggesting the reliability of our designed system.