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The emissions from the first luminous sources drive the fluctuations in the 21-cm signal at Cosmic Dawn (CD) via two main astrophysical processes, namely Ly alpha coupling and X-ray heating, yielding a highly non-Gaussian signal. The impact of these processes on the 21-cm signal and its non-Gaussianity depends on the properties of these first sources of light. In this work, we consider different CD scenarios by varying two major source parameters i.e. the minimum halo mass M-h,M-min and X-ray photon production efficiency fX using the 1D radiative transfer code grizzly. We study the impact of variation in these source parameters on the large scale ( k(1) = 0.16Mpc(-1)) 21-cm bispectrum for all possible unique triangles in the Fourier domain. Our detailed and comparative analysis of the power spectrum and bispectrum shows that the shape, sign and magnitude of the bispectrum jointly provide a better measure of the signal fluctuations and its non-Gaussianity than the power spectrum alone. We also conclude that it is important to study the sequence of sign changes along with the variations in the shape and magnitude of the bispectrum throughout the CD history to arrive at a robust conclusion about the dominant processes in the intergalactic medium at different cosmic times. We further observe that among all the possible unique k-triangles, the large-scale non-Gaussianity of the signal is best probed by the small k-triangles in the squeezed limit and by triangle shapes in its vicinity. This opens up the possibility of constraining the source parameters during the CD using the 21-cm bispectrum.