The remarkable photonic and photochemical properties of colloidal quantum dots (QD) depend critically on the dynamics of carrier interactions and relaxation. Despite their importance, a quantitative experimental evaluation of these processes has proven elusive due to the inherent challenge of exactly separating single-exciton and multi-exciton dynamics, whose spectroscopic signatures overlap in time, spectrum, and excitation fluence. Here, we measure pump fluence-dependent absolute pump-probe transients of indium arsenide QDs, refreshing the sample using beam scanning to limit repetitive excitation. Focusing on the low fluence limit near the onset of bi-exciton formation, excitation conditions were precisely controlled and characterized by averaging Poisson-distributed excitation statistics over all three spatial dimensions of the pump and probe beam spatial profiles to determine the average excitation probability. A saturation model is developed to uniquely decompose the pump-probe signal into single-exciton and bi-exciton signals. This method harnesses the distinct pump-fluence scaling of absolute pump-probe signals from singly- and doubly-excited QDs without any assumptions regarding the relative timescales or amplitudes of single-exciton and bi-exciton signals. Probing in the bulk-like region of the QD absorption spectrum, the signal from bi-excitons is found to be 1.8 times the signal from single excitons at T = 0, consistent with the conventionally assumed factor of 2 within the 95% confidence intervals. The bi-exciton signal contains the same hot carrier relaxation dynamics as that from single excitons, but signal from a second exciton additionally exhibits a 26 ps exponential decay attributed to Auger recombination.