Bipolar membranes (BPMs) are increasingly recognized as a promising electrolyte option for water electrolysis, attributable to their distinctive properties derived from the membrane’s layered structure, which consists of an anion exchange (AEL) and a cation exchange layer (CEL). This study investigates four different BPMs and the influence they have on the performance of a water electrolysis cell under two different feed configurations: (1) a symmetric deionized water feed to both anode and cathode compartments and (2) an asymmetric feed with a 0.5 mol/L NaCl catholyte feed and a deionized water anolyte feed. The BPMs were also investigated for total chlorine (Cl) species (e.g., Cl–, Cl2, HOCl, and ClO–) in the anolyte due to Cl– crossover from the catholyte during water electrolysis with the asymmetric feed, at an applied current density of 250 mA/cm2. The best-performing BPM with the asymmetric feed was an E98-05 (CEL)/FAS-50 (AEL) membrane with a TiO2 water dissociation catalyst at the BPM junction. This membrane had the lowest measured Cl species crossover and lowest cell voltage at a given current density under asymmetric conditions compared to the other BPMs studied. It was also found that under asymmetric conditions the CEL facing the catholyte feed determined the amount of total Cl species crossover due to anion exclusion (Donnan exclusion) of the CEL, reducing the amount of Cl– in the CEL where it crossed over to the AEL and the anolyte compartment.