The study of binding kinetics via the analysis of fluorescence time traces is often con-founded by measurement noise and photophysics. Although photoblinking can be mitigated by using labels less likely to photoswitch, photobleaching generally cannot be eliminated. Current methods for measuring binding and unbinding rates are therefore limited by concurrent photobleaching events. Here, we propose a method to infer binding and unbinding rates alongside photobleaching rates using fluorescence intensity traces. Our approach is a two-stage process involving analyzing individual regions of interest (ROIs) with a Hidden Markov Model to infer the fluorescence intensity levels of each trace. We then use the inferred intensity level state trajectory from all ROIs to infer kinetic rates. Our method has several advantages, including the ability to analyze noisy traces, account for the presence of photobleaching events, and provide uncertainties associated with the inferred binding kinetics. We demonstrate the effectiveness and reliability of our method through simulations and data from DNA origami binding experiments.