A phenomenological picture of a pulsed electrical discharge in gas bubbles in water is produced by combining electrical, spectroscopic, and imaging characterization methods. The discharge is generated by applying 1 mu s pulses of 5 to 20 kV between a needle and a disk electrode submerged in water. An Ar gas bubble surrounds the tip of the needle electrode. Imaging, electrical characteristics, and time-resolved optical emission spectroscopic data suggest a fast streamer propagation mechanism and the formation of a plasma channel in the bubble. Comparing the electrical and imaging data for consecutive pulses applied to the bubble at a frequency of 1 Hz indicates that each discharge proceeds as an entirely new process with no memory of the previous discharge aside from the presence of long-lived chemical species, such as ozone and oxygen. Imaging and electrical data show the presence of two discharge events during each applied voltage pulse, a forward discharge near the beginning of the applied pulse depositing charge on the surface of the bubble and a reverse discharge removing the accumulated charge from the water/gas interface when the applied voltage is turned off. The pd value of similar to 300-500 torr cm, the 1 mu s long pulse duration, low repetition rate, and unidirectional character of the applied voltage pulses make the discharge process here unique compared to the traditional corona or dielectric barrier discharges.