We study the effect of near-resonant optical injection on the dynamical behavior of an erbium-doped fiber ring laser. Our experimental results show that, in the presence of even a small amount of injection, the output laser intensity exhibits bursts spaced irregularly in time and with randomly varying amplitudes. A heterodyne measurement of the frequency dynamics of the laser suggests that this bursting is due to an irregular wandering of the laser frequency through the injection locking range. This interpretation is confirmed by a systematic analysis of a simplified rate-equation model in which the frequency wandering is modeled phenomenologically by means of a temporally correlated noise. A statistical analysis of the bursting events is performed, displaying satisfactory agreement between the experiment and the model. In particular, the interburst time distribution exhibits a well defined power law decay over a sizable time range.