We have established the stability and range of the cubic type II phase of Bi1 - xWxO1.5 (+ 1.5x) using a combination of X-ray diffraction, neutron diffraction and X-ray absorption spectroscopy. Type II is a high temperature modification that can be obtained by quenching/rapid cooling of samples with compositions between x = 0.148 to x = 0.185. Slower cooling rates yield the stable low temperature polymorph, the tetragonal type Ib phase (Bi rich samples), and mixtures of type Ib and Aurivillius phase (W-rich samples). Throughout the entire solid solution range, type II exhibits a (3 + 3) dimensional incommensurate modulation with modulation vectors slightly smaller than 1/3 based on a cubic fluorite type subcell (delta-Bi2O3). The main structural motifs are well-defined tetrahedra of WO6 octahedra in a delta-Bi2O3-matrix, with additional W being incorporated on corners and face centers of the approximate commensurate 3 x 3 x 3 supercell in octahedral coordination, confirmed by XANES analysis of the W L-3-edge. Impedance measurements reveal oxide ionic conductivities comparable to those of yttria-stabilised zirconia even after a decrease in ionic conductivity of about half an order of magnitude on thermal cycling due to transition to the tetragonal type Ib phase.