Single photon counting time distributions obtained from single molecule photon arrival trajectories are employed in the theoretical study of multistate kinetics coupled to a two-state jump bath. The bath time scale may be extracted from statistical analysis of one- and two-point time-domain optical measurements. The amplitude and shape of the distribution of interphoton arrival times reflects bath correlations. A slow bath (relative to the kinetics) results in broad distributions of arrival times reflecting bath memory. For a fast bath, the arrival time distributions narrow around shorter times, similar to motional narrowing in frequency domain spectroscopy. The variance of either kinetic rates or equilibrium population of bath states results in asymmetry of the distribution of two photon arrival times.