CO₂ electrolysis is a promising process to produce synthetic and carbon-neutral chemicals. Zero-gap CO₂ electrolyzers featuring a forward bias bipolar membrane (BPM) solve problems like salt precipitation and CO₂ crossover but still suffer from limited performance and durability. Their relatively low efficiency could be attributed to water management: excess in the diffusion media causing flooding or deficit for the CO₂ reduction reaction. This work investigates the main water transport mechanisms, including identifying water sources and sinks and the experimental analysis of the diffusive transport and sorption in the BPM. Operando x-ray tomography reveals water distribution within the gas diffusion media and membrane swelling behavior. The set of experiments shows the intrinsic limitations of the forward bias BPM cell at industrially relevant current densities: insufficient water supply for the cathode reaction and current-driven BPM over-swelling. GDL flooding can be excluded as a limitation at the investigated current densities.