© 2017 The Authors. We study the structure of the inner Milky Way using the latest data release of the VISTA Variables in the Via Lactea (VVV) survey. The VVV is a deep near-infrared, multi-colour photometric survey with a coverage of 300 square degrees towards the bulge/bar. We use red clump (RC) stars to produce a high-resolution dust map of the VVV's field of view. From dereddened colour-magnitude diagrams, we select red giant branch stars to investigate their 3D density distribution within the central 4 kpc. We demonstrate that our best-fitting parametric model of the bulge density provides a good description of the VVV data, with a median percentage residual of 5 per cent over the fitted region. The strongest of the otherwise lowlevel residuals are overdensities associated with a low-latitude structure as well as the so-called X-shape previously identified using the split RC. These additional components contribute only ~5 per cent and ~7 per cent respectively to the bulge mass budget. The best-fitting bulge is 'boxy' with an axial ratio of [1:0.44:0.31] and is rotated with respect to the Sun-Galactic Centre line by at least 20°. We provide an estimate of the total, full sky, mass of the bulge of MbulgeChabrier= 2.36 × 1010M⊙for a Chabrier initial mass function. We show that there exists a strong degeneracy between the viewing angle and the dispersion of the RC absolute magnitude distribution. The value of the latter is strongly dependent on the assumptions made about the intrinsic luminosity function of the bulge.