Two dynamical systems unidirectionally coupled in a sender-receiver configuration can synchronize with a nonzero phase-lag. In particular, the system can exhibit anticipated synchronization (AS), which is characterized by a negative phase-lag, if the receiver (R) also receives a delayed negative self-feedback. Recently, AS was shown to occur between cortical-like neuronal populations in which the self-feedback is mediated by inhibitory synapses. In this biologically plausible scenario, a transition from the usual delayed synchronization (DS, with positive phase-lag) to AS can be mediated by the inhibitory conductances in the receiver population. Here we show that depending on the relation between excitatory and inhibitory synaptic conductances the system can also exhibit phase-bistability between anticipated and delayed synchronization. Furthermore, we show that the amount of noise at the receiver and the synaptic conductances can mediate the transition from stable phase-locking to a bistable regime and eventually to a phase-drift (PD). We suggest that our spiking neuronal populations model could be potentially useful to study phase-bistability in cortical regions related to bistable perception.