Sustained neuronal activity can be broadly classified as either tonic firing or bursting. These two major patterns of neuronal oscillations are state dependent and may coexist. The dynamics and intracellular mechanisms of transitions between tonic firing and bursting in cortical networks remain poorly understood. Here we describe a detailed two-compartment conductance-based cortical neuron model which exhibits bistability with hysteresis between tonic firing and bursting for elevated extracellular potassium concentration. The study explains the ionic and dynamical mechanisms of burst generation and reveals the conditions underlying coexistence of two different oscillatory modes as a function of neuronal excitability.