In underwater wireless optical communications (UWOC), the random obstruction of light propagation by air bubbles can cause fluctuations in the incoming light intensity of a receiver. In this paper, we propose a statistical model for determining the received power by a receiver in the presence of air bubbles. First, based on real experiments of the behavior of air bubbles underwater, we propose statistical models for the generation, size, and horizontal distribution of each air bubble. Second, we mathematically derive the obstruction caused by the shadow of each bubble as it passes over the beam area. We then compute the combined obstruction of all generated air bubbles to determine the total obstructed power, which is a random variable due to the randomness of bubble behavior. Next, we find the first and second moments of the total obstructed power to model the statistical distribution of the obstructed received power by using the method of moments, which shows that the Weibull distribution suitably matches the simulation data. We also estimate the shape and scale parameters by using two derived moments. Furthermore, we also construct a statistical model of the received power with complete blockage in the presence of air bubbles and we derive the distribution of the composite channel model combining the proposed bubble-obstruction model with a Gamma-Gamma turbulence model. Finally, we obtain and verify the analytic forms of the average bit error rate and the capacity of UWOC systems under this newly proposed composite channel model.