For the first time since 1992 when the Pioneer Venus Orbiter (PVO) ceased to operate, there is again a plasma instrument in orbit around Venus, namely the ASPERA-4 flown on Venus Express (inserted into an elliptical polar orbit about the planet on April 11, 2006). In this paper we report on measurements made by the ion and electron sensors of ASPERA-4 during their first five months of operation and, thereby, determine the locations of both the Venus bow shock (BS) and the ion composition boundary (ICB) under solar minimum conditions. In contrast to previous studies based on PVO data, we employ a 3-parameter fit to achieve a realistic shape for the BS. We use a different technique to fit the ICB because this latter boundary cannot be represented by a conic section. Additionally we investigate the dependence of the location of the BS on solar wind ram pressure (based on ASPERA-4 solar wind data) and solar EUV flux (using a proxy from Earth).