The application of temperature-programmed desorption (TPD) techniques in heterogeneous catalysis to probe, among other things, the nature of the reactions on the surface solid catalyst, and ultimately, the kinetics of desorbed species, is hampered by the inability to make direct observations of adsorbates when they are most catalytically active. Thus, it is almost impossible to make a direct association between a given elementary surface process and a key feature on the TPD spectra, such as the nature and number of peaks. What kinetic Monte Carlo simulations have shown, on the other hand, is that the complex surface evolution during TPD is controlled effectively by just a few parameters that relate to the surface kinetics and energetics. In this study, we will use kinetic Monte Carlo approach to show that double-peaked TPD spectra obtained from adsorption of Bi adsorbates on Ni(100) at an initial temperature of 800 K and subsequent TPD runs for high preadsorbed coverages can indeed be explained satisfactorily by assuming predominant first-order desorption kinetics coupled with adsorbate-adsorbate lateral interactions, in agreement with prior studies. While not totally discounting the presence of Bi dimers, and thus second-order desorption, our study is sensitive enough to reveal the extent of their presence. In other words, we propose that dimers can coexist with Bi adatoms in small amounts while retaining the key features of the TPD spectra, provided the kinetic parameters associated with dimer formation (and dissolution) are well within a certain range. On the other hand, any model in which dimers are present to a degree in which they are not totally dominated by adatoms cannot produce TPD spectra that are consistent with the experiment.