Many bacteria swim by rotating a helical flagellar filament attached to a bacterial flagellar motor embedded in the cell wall. Common motility patterns of bacteria involve longer, relatively straight runs interspersed with reorientation events. The reorientation events are associated with reversals of the flagellar motor, but otherwise the motor has usually been considered to rotate with constant torque and speed during runs. We report observations of fluctuations in swimming speed during runs of the singly-flagellated bacterium Vibrio anguillarum. We show that these ~100 ms fluctuations in swimming speed are associated with fluctuations in the rotation speed and torque of the bacterial flagellar motor, indicating that the behavior of the flagellar motor is more variable than often thought.