We study the three-dimensional Morris–Lecar–Terman neuron model in the parametric region of tonic spiking oscillations close to the bifurcation of the torus birth. It is shown that in this region random disturbances can induce switching to the toroidal bursting mode from the tonic spiking regime. We approximate the probability of such switches as well as analyze temporal characteristics of produced oscillations. Moreover, we indicate a coherence resonance in the stochastic bursting regime and reveal the underlying reasons of these noise-induced phenomena.