We present a single-cell motility assay, which allows the quantification of bacterial swimming in a well-controlled environment, for durations of up to an hour and with a temporal resolution greater than the flagellar rotation rates of approximately 100 Hz. The assay is based on an instrument combining optical tweezers, light and fluorescence microscopy, and a microfluidic chamber. Using this device we characterized the long-term statistics of the run-tumble time series in individual Escherichia coli cells. We also quantified higher-order features of bacterial swimming, such as changes in velocity and reversals of swimming direction.