A simple model is employed to explain the anomalous surface-flashover characteristics observed when insulators in vacuum are stressed with bipolar voltage waveforms. Under unipolar stress, the flashover field is found to vary as the inverse square root of the prebreakdown time delay over the first few tens of nanoseconds, thereafter becoming less dependent on delay. The short-delay behavior, according to our model, results from the accumulation of ionic charge adjacent to the insulator-vacuum interface. At longer delays ions are swept away nearly as rapidly as they are created. Flashover data from conventional insulator assemblies subjected to unipolar stress is consistent with ions being swept away. With the application of a roughly 10 MHz, bipolar voltage waveform a different behavior is observed. The holdoff is unexpectedly low and an anomalous inverse-square-root dependence on delay persists over hundreds of nanoseconds. Analysis of ion motion indicates that some fraction of the ions follow small-amplitude oscillatory trajectories and continue to accumulate for relatively long periods of time. An insulator has been modified to enhance ion removal by decreasing the thickness of polystyrene segments fourfold to 4.7 mm. A 50% improvement in performance is found, although the holdoff remains below standards applicable to unipolar stress.