Single quantum emitters of light are valuable resources for engineered quantum systems. They can function as robust single-photon generators, allow optical control of single spins, provide readout capabilities for atomic-scale sensors, and provide interfaces between stationary and flying qubits. Environmental factors can lead to single emitters exhibiting "blinking", whereby the fluorescence level switches between "on" and "off" states. Detailed characterisation of this blinking behaviour is often a powerful way to gain understanding about the underlying physical mechanisms, and determining the switching rates is typically desired. Bright emitters lead to high-contrast blinking, and simple thresholds can be used to extract the "on" and "off" intervals from a time-series of photon counts (and hence determine the switching rates). However, such approaches become difficult for emitters fluorescing at low levels. We have developed a Bayesian approach capable of inferring switching rates directly from the time-series. This is able to produce useful results even for weak blinking fluorescence traces with considerable background photon counts. Moreover, the Bayesian inference also yields a robust picture of the parameter uncertainties, providing a benefit also for bright emitters.