Spin-crossover (SCO) molecules are versatile magnetic switches with applications in molecular electronics and spintronics. Downscaling devices to the single-molecule level remains, however, a challenging task since the switching mechanism in bulk is mediated by cooperative intermolecular interactions. Here, we report on electron transport through individual Fe-SCO molecules coupled to few-layer graphene electrodes via π-π stacking. We observe a distinct bistability in the conductance of the molecule and a careful comparison with density functional theory (DFT) calculations allows to associate the bistability with a SCO-induced orbital reconfiguration of the molecule. We find long spin-state lifetimes that are caused by the specific coordination of the magnetic core and the absence of intermolecular interactions according to our calculations. In contrast with bulk samples, the SCO transition is not triggered by temperature but induced by small perturbations in the molecule at any temperature. We propose plausible mechanisms that could trigger the SCO at the single-molecule level.