With its high mobility, narrow bandgap, and unique anisotropy, black phosphorus (BP) is a promising material for optoelectronic applications. Waveguide-integrated photodetectors with RC-limited speeds up to 3 GHz have been recently demonstrated at telecom wavelengths. To truly be competitive, however, BP photodetectors must reach speeds of tens of GHz. Here, we use BP's nonlinear photoresponse to measure the intrinsic speed of a BP photodetector using ultrafast pump-probe measurements. With this technique, we are able to observe how the detection speed depends on both the incident power and applied source-drain bias. A minimum response time of 60 ps was observed which corresponds to an intrinsic bandwidth of 9 GHz.