We have investigated ion current rectification properties of a recently prepared bipolar nanofluidic diode. This device is based on a single conically shaped nanopore in a polymer film whose pore walls contain a sharp boundary between positively and negatively charged regions. A semi-quantitative model that employs Poisson and Nernst-Plank equations predicts current-voltage curves as well as ionic concentrations and electric potential distributions in this system. We show that under certain conditions the rectification degree, defined as a ratio of currents recorded at the same voltage but opposite polarities, can reach values of over a 1000 at a voltage range <-2 V, +2 V>. The role of thickness and position of the transition zone on the ion current rectification is discussed as well. We also show that rectification degree scales with the applied voltage.