We compute the bispectra of the 21cm signal during the Epoch of Reionization for three different reionization scenarios that are based on a dark matter N-body simulation combined with a self-consistent, semi-numerical model of galaxy evolution and reionization. Our reionization scenarios differ in their trends of ionizing escape fractions ($f_mathrm{esc}$) with the underlying galaxy properties and cover the physically plausible range, i.e. $f_mathrm{esc}$ effectively decreasing, being constant, or increasing with halo mass. We find the 21cm bispectrum to be sensitive to the resulting ionization topologies that significantly differ in their size distribution of ionized and neutral regions throughout reionization. From squeezed to stretched triangles, the 21cm bispectra features a change of sign from negative to positive values, with ionized and neutral regions representing below-average and above-average concentrations contributing negatively and positively, respectively. The position of the change of sign provides a tracer of the size distribution of the ionized and neutral regions, and allows us to identify three major regimes that the 21cm bispectrum undergoes during reionization. In particular the regime during the early stages of reionization, where the 21cm bispectrum tracks the peak of the size distribution of the ionized regions, provides exciting prospects for pinning down reionization with the forthcoming Square Kilometre Array.