In ensembles of oscillators, intrinsic fluctuations often enable nontrivial dynamics in seemingly simple situations. One of such effects occurs in coupled FitzHugh-Nagumo oscillators subjected to external noise. At the considered parameter values, the global deterministic attractor is the resting state. Additive noise invokes transient bursting: series of intermittent patches of spikes, followed by the abrupt decay to rest. Duration of this transient, small for weak noise, asymptotically diverges when the noise becomes stronger. Remarkably, in repeated trials at fixed parameters, the number of bursts until the ultimate decay strongly varies. Lifetime statistics for this transient in large ensembles of numerical realizations features the exponential distribution. Observations on transient bursting are confirmed by experiments with coupled analog electronic circuits, modeling the FitzHugh-Nagumo dynamics. We relate the exponential character of the distribution to the probability that the system, disturbed by noise, escapes the local attraction basin of the resting state.