Experiments were carried out on bursting oscillations in an electrochemical system, the dissolution of iron in sulfuric acid. Bursting characteristics were investigated as functions of the parameters applied potential and external resistance. We develop a model that incorporates the effects of oxide and salt films. This model reproduces all the important features of the dynamics seen in experiments including both the slow active-passive oscillations and the faster oscillations on the mass-transfer-limited plateau as well as the bursting phenomena. During this bursting, two time scales are important: the slow variation of the salt-film thickness and the faster dynamics of a three-variable (potential drop and proton and iron(II) concentrations) subsystem.