In this paper, we perform a complete one-loop computation of the short-distance Wilson coefficients for B-s,B-d - (B) over bar (s,d) mixings and B-s,B-d -> l(+)l(-) decays in the Manohar-Wise model, which extends the Standard Model ( SM) scalar sector by a colour-octet and weak-doublet scalar. Based on these calculations, combined constraints on the model parameters are derived from the current flavour data, including the B-s,B-d - (B) over bar (s,d) mixings, B-s,B-d -> mu(+)mu(-), B -> X-s gamma, B -> K*gamma, B -> rho gamma, and Z -> b (b) over bar decays. The future sensitivity to the model...