In this paper, motivated by the observation that the Standard Model predictions are now above the experimental data for the mass difference M-s(d), we perform a detailed study of B-s(d) - B-s(d) mixing and B-s (+-) decay in the Z(3)-invariant NMSSM with non-minimal flavour violation, using the recently developed procedure based on the Flavour Expansion Theorem, with which one can perform a purely algebraic mass-insertion expansion of an amplitude written in the mass eigenstate basis without performing any diagrammatic calculations in the interaction/flavour basis. Specifically, we consider the...