The quality of sensing and response to external stimuli constitutes a basic element in the selective performance of living organisms. Here we consider the response of Escherichia coli to chemical stimuli. For moderate amplitudes, the bacterial response to generic profiles of sensed chemicals is reconstructed from its response function to an impulse, which then controls the efficiency of bacterial motility. We introduce a method for measuring the impulse response function based on coupling microfluidic experiments and inference methods: The response function is inferred using Bayesian methods from the observed trajectories of bacteria swimming in microfluidically controlled chemical fields. The notable advantages are that the method is based on the bacterial swimming response, it is noninvasive, without any genetic and/or mechanical preparation, and assays the behavior of the whole flagella bundle. We exploit the inference method to measure responses to aspartate and α-methylaspartate--measured previously by other methods--as well as glucose, leucine, and serine. The response to the attractant glucose is shown to be biphasic and perfectly adapted, as for aspartate. The response to the attractant serine is shown to be biphasic yet imperfectly adapted, that is, the response function has a nonzero (positive) integral. The adaptation of the response to the repellent leucine is also imperfect, with the sign of the two phases inverted with respect to serine. The diversity in the bacterial population of the response function and its dependency upon the background concentration are quantified.