We report time-resolved measurements of magnetization switching by spin-orbit torques in the absence of an external magnetic field in perpendicularly magnetized magnetic tunnel junctions (MTJ). Field-free switching is enabled by the dipolar field of an in-plane magnetized layer integrated above the MTJ stack, the orientation of which determines the switching polarity. Real-time single-shot measurements provide direct evidence of magnetization reversal and switching distributions. Close to the critical switching voltage we observe stochastic reversal events due to a finite incubation delay preceding the magnetization reversal. Upon increasing the pulse amplitude to twice the critical voltage the reversal becomes quasi-deterministic, leading to reliable bipolar switching at sub-ns timescales in zero external field. We further investigate the switching probability as a function of dc bias of the MTJ and external magnetic field, providing insight on the parameters that determine the critical switching voltage.