Inner belt energetic protons are a hindrance to development of space technologies. The emission of electromagnetic ion cyclotron (EMIC) waves from spaceborne transmitters has been proposed as a way to solve this problem. The interaction between particles and narrowband emissions has been typically studied using nonlinear test particle simulations. We show that this formulation results in a random walk of the inner belt protons in velocity space. In this paper we compute bounce-averaged pitch angle diffusion rates from test particle simulations and compare them to those of quasi-linear theory for quasi-monochromatic EMIC waves interacting with inner belt protons. We find that the quasi-linear solution is not sensitive to the frequency bandwidth for narrow distributions. Bounce-averaged diffusion coefficients from both approaches are in good agreement for all energies and pitch angles. The interaction with inner belt protons, therefore, can be addressed using quasi-linear diffusion codes, which allows faster exploration of parameter space.