A plethora of recent experimental literature implicates the abrupt, synchronous activation of GABAergic interneurons in driving the sudden change in brain activity that heralds seizure initiation. However, the mechanisms predisposing an inhibitory network toward sudden coherence specifically during ictogenesis remain unknown. We address this question by comparing simulated inhibitory networks containing control interneurons and networks containing hyper-excitable interneurons modeled to mimic treatment with 4-Aminopyridine (4-AP), an agent commonly used to model seizures \textit{in vivo} and \textit{in vitro}. Our \textit{in silico} study demonstrates that model inhibitory networks with 4-AP interneurons are more prone than their control counterparts to exist in a bistable state in which asynchronously firing networks can abruptly transition into synchrony due to a brief perturbation. We further show that perturbations driving this transition could reasonably arise \textit{in vivo} based on models of background excitatory synaptic activity in the cortex. Thus, these results propose a mechanism by which an inhibitory network can transition from incoherent to coherent dynamics in a fashion that may precipitate seizure as a downstream effect. Moreover, this mechanism specifically explains why inhibitory networks containing hyper-excitable interneurons are more vulnerable to this state change, and how such networks can undergo this transition without a permanent change in the drive to the system. This, in turn, potentially explains such networks' increased vulnerability to seizure initiated by GABAergic activity.