In this paper, we present an analytical model for a diffusive molecular communication (MC) system with a reversible adsorption receiver in a fluid environment. The time-varying spatial distribution of the information molecules under the reversible adsorption and desorption reaction at the surface of a bio-receiver is analytically characterized. Based on the spatial distribution, we derive the number of newly-adsorbed information molecules expected in any time duration. Importantly, we present a simulation framework for the proposed model that accounts for the diffusion and reversible reaction. Simulation results show the accuracy of our derived expressions, and demonstrate the positive effect of the adsorption rate and the negative effect of the desorption rate on the net number of newly-adsorbed information molecules expected. Moreover, our analytical results simplify to the special case of an absorbing receiver.