We report measurements of Shubnikov-de Haas oscillations in the giant Rashba semiconductor BiTeI under applied pressures up to similar to 2GPa. We observe one high frequency oscillation at all pressures and one low frequency oscillation that emerges between similar to 0.3-0.7 GPa indicating the appearance of a second small Fermi surface. BiTeI has a conduction band bottom that is split into two sub-bands due to the strong Rashba coupling, resulting in a 'Dirac point'. Our results suggest that the chemical potential starts below the Dirac point in the conduction band at ambient pressure and moves upward, crossing it as pressure is increased. The presence of the chemical potential above this Dirac point results in two Fermi surfaces. We present a simple model that captures this effect and can be used to understand the pressure dependence of our sample parameters. These extracted parameters are in quantitative agreement with first-principles calculations and other experiments. The parameters extracted via our model support the notion that pressure brings the system closer to the predicted topological quantum phase transition.