A charge control model for the transient analysis of the bipolar transistor laser in forward active mode is developed to describe the dynamics of electron, photon and charge densities. From three coupled-rate equations, analytical expressions are obtained for the threshold base current density, the steady-state electron and photon densities, and small-signal frequency response. We find that the threshold current density decreases with increasing spontaneous emission lifetime of electrons in the quantum well as well as a linear dependence of the photon density on the base current. By optimizing the model parameters in their physical range, we show that a -3-dB bandwidth of 55 GHz can be achieved for small-signal modulation of the laser. By numerically solving the rate equations, we investigate the -3-dB bandwidth under large-signal modulation to show that it remains nearly unchanged from the small-signal case. We further perform analysis of laser switching and find that the turn-on time is reduced by increasing the base current or decreasing the spontaneous emission lifetime of electrons in the quantum well.