Bipolar electrodes provide a powerful and versatile means of coupling two or more spatially separated electrochemical reactions. While normally described in terms of macroscopic rate equations, the ongoing drive toward the miniaturization of bipolar electrodes means that new regimes are becoming accessible where stochasticity and the discreteness of the electronic charge become relevant or even dominant. Here we explore using both numerical simulations and analytical theory the behavior of bipolar electrodes with nanoscale dimensions. We focus in particular on the possibility of achieving single-molecule-level synchronization between the two poles of a bipolar electrode, which would dramatically extend the range of applicability of single-molecule electrochemistry. We conclude that, while possible, fundamental limits on the potential dependence of electron-transfer rates dictate that this will only be achieved in the smallest (less than 10 nm) bipolar nanoelectrodes.