Using high resolution x-ray diffraction data, we show that the composition dependence of the normalized basal-spacing,dN(x), of the bi-layer alkali perovskites, CsxRb1-x[LaNb2O7], measured over the range 0≤x≤1, can be quantitatively accounted for with the anharmonic Lennard-Jones (aLJ) model which incorporates deformations ofboththe host layers and the guest ions. With the same independently determined value of the Rb/Cs stiffness constant ratio, 1.73, used in previous studies of CsxRb1-x[Ca2Nb3O10], the tri-layer perovskites, the aLJ model yields a very good one-parameter fit todN(x) for the bi-layer perovskites. The single fitting parameter, β = [d(0)-t]/[d(1) -t] wheretis the host layer thickness, yields atvalue of 7.73Å in very good (3%) agreement with the value 7.97Å deduced from structural studies.