We report an automated microfluidic platform for 'digitally' screening the composition space of droplets containing cocktails of small molecules and demonstrate the features of this system by studying epistatic interactions between antibiotics and Escherichia coli ATCC 25922. This system has several key characteristics: (i) it uses small (<100 μL) samples of liquids and suspensions of bacteria that are introduced directly into the chip; (ii) it generates a sequence of droplets with compositions, including reagents and bacterial cell suspensions that are programmed by the user; (iii) it exports the sequence of droplets to an external segment of tubing that is subsequently disconnected for incubation and storage; and (iv) after incubation of bacteria in droplets, the droplets are injected into a second device equipped with an in-line fiber optic spectrophotometer that measures cell growth. The system generates and fuses droplets with precise (<1% in standard deviation) control of liquid volumes and of the concentrations of input substrates. We demonstrate the application of this technology in determining the minimum inhibitory concentration and pair-wise interactions of ampicillin, tetracycline, and chloramphenicol against E. coli. The experiments consumed small volumes of reagents and required minutes to create the droplets and several hours for their incubation and analysis.