Synthetic biologists increasingly rely on directed evolution to optimize engineered biological systems. Applying an appropriate screening or selection method for identifying the potentially rare library members with the desired properties is a crucial step for success in these experiments. Special challenges include substantial cell-to-cell variability and the requirement to check multiple states (e.g., being ON or OFF depending on the input). Here, we present a high-throughput screening method that addresses these challenges. First, we encapsulate single bacteria into microfluidic agarose gel beads. After incubation, they harbor monoclonal bacterial microcolonies (e.g., expressing a synthetic construct) and can be sorted according their fluorescence by fluorescence activated cell sorting (FACS). We determine enrichment rates and demonstrate that we can measure the average fluorescent signals of microcolonies containing phenotypically heterogeneous cells, obviating the problem of cell-to-cell variability. Finally, we apply this method to sort a pBAD promoter library at ON and OFF states.