The fluorite structured mixed metal fluorides Rb1-xBixF1+2x (0.5 less-than-or-equal-to x greater-than-or-equal-to 0.75) are exceptionally good F- ion conductors, a property which is clearly related to the mixed nature of the cation sub-lattice. Extended X-ray absorption fine structure (EXAFS) has been used to study the local structure of the two types of cation in Rb1-xBixF1+2x as a function of x. The results reveal marked differences for the local environments of Rb+ and Bi3+. Considerable short-range order develops as x deviates from 0.5, and this can be correlated with the relative conductivities of these materials. Molecular dynamics (MD) has been used to yield complementary information on structural properties. Simulations were performed for a series of temperatures between 80 K and 750 K. Excellent agreement between EXAFS and MD is obtained. A non-collinear interstitialcy mechanism is proposed for anion diffusion, which is seen to be the basis for more complex concerted processes.