Polyaniline-based composites serve as adsorbent materials for the removal of hazardous heavy metal impurities such as Cr(VI) from wastewater. However, previous reports on polyaniline (PANi)-based adsorbents mainly focus on Cr(VI) removal from acidic aqueous solutions (pH 1–5). Nonetheless, in the case of potable water, Cr(VI) removal has to be performed at neutral pH. In this study, we demonstrate the removal of Cr(VI) from drinking water at neutral pH using a PANi/bacterial cellulose (BC) mat. The rate-limiting step observed at neutral pH is the desorption of reduced Cr(III) from the PANi/BC adsorbent. This is contrary to that observed in acidic solution, where the adsorption of Cr(VI) is reported to be the slowest step. The aforementioned claim is confirmed by applying the Langmuir–Hinshelwood kinetic model to the adsorption–reduction–desorption processes.