We present measurements of the dark matter bispectrum in N-body simulations with non-Gaussian initial conditions of the local kind for a large variety of triangular configurations and compare them with predictions from Eulerian perturbation theory up to one-loop corrections. We find that the effects of primordial non-Gaussianity at large scales, when compared to perturbation theory, are well described by the initial component of the matter bispectrum, linearly extrapolated at the redshift of interest. In addition, we find that for fNL = 100, the non-linear corrections due to non-Gaussian initial conditions are of the order of ~3-4 per cent for generic triangles and up to ~20 per cent for squeezed configurations, at any redshift. We show that the predictions of perturbation theory at the tree level fail to describe the simulation results at redshift z = 0 at scales corresponding to k ~ 0.02-0.08hMpc-1, depending on the triangle, while one-loop corrections can significantly extend their validity to smaller scales. At higher redshift, one-loop perturbation theory indeed provides quite accurate predictions, particularly with respect to the relative correction due to primordial non-Gaussianity.