To calculate the impulse response of a bubble cloud in a compressible medium, a methodology is developed that incorporates multiple scattering effects between bubbles and coherent interactions of their individual scattered fields. This method is based on a perturbation theory, and provides for an approximate solution formulated by adding a perturbation to the mathematical description of a linear problem. The solution is defined as a power series, where the first term of the expansion corresponds to the solution of a linear uncoupled equation. The convergence of the expansion is determined by the parameters of the physical bubbles and the acoustic interactions. The model is successfully applied to describe experimental measurements of a model bubble cloud response in a shallow freshwater environment.