Bipolar-membrane electrodialysis (BPM-ED) carbon capture uses renewable electricity to drive the capture and release of carbon dioxide (CO2), making it a potentially important tool in the fight against climate change. This process employs BPMs to generate pH-swings for CO2 capture and has been demonstrated at the lab scale at current densities exceeding 100 mA cm -2 . However, the energy required to drive BPM-ED (>300 kJ mol -1 ) is prohibitive for industrial deployment. This study optimizes BPM-ED using a continuum modeling approach validated by experiment, which quantifies the energy intensity of BPM-ED and resolves the transport and dynamic equilibrium of reactive carbon species in BPMs. Applied-voltage-breakdown analysis identifies the dominant energy losses and elucidates BPM properties that improve the efficiency of BPM-ED. The model reveals that mitigation of generated CO2 bubbles and acceleration of water-dissociation catalysis could reduce the energy intensity to <80 kJ mol -1 at 100 mA cm -2 , demonstrating potential for achieving high rates with substantially reduced energy penalties. This study provides insights into the physics of BPMs immersed in reactive carbon solutions and contributes towards the development of BPMs for electrochemical CO2 reduction, cement production, and other emerging electrochemically decarbonized applications.