A cellular automaton (CA) model is proposed in this paper to analyze a bridge traffic bottleneck. The simulation results with this model show that there are several phase transitions in the traffic average density, velocity and flow for each lane under a periodic boundary condition. An unstable phase in the traffic average density and velocity for the upstream and downstream lanes of the bridge is shown in a range of initial traffic densities. The critical points of the phase transitions and the phenomenon of the unstable phase found in the simulation are also explained with the mean-field theory.