  In this paper, we perform a complete one-loop computation of the
short-distance Wilson coefficients for $B_{s,d}-\bar{B}_{s,d}$ mixings and
$B_{s,d}\to\ell^+\ell^-$ decays in the Manohar-Wise model, which extends the 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 $B_{s,d}-{\bar{B}}_{s,d}$ mixings,
$B_{s,d}\to\mu^+\mu^-$, $B\to X_s\gamma$, $B\to K^{\ast}\gamma$,
$B\to\rho\gamma$, and $Z\to b \bar{b}$ decays. The future sensitivity to the
model is also explored in the observables achievable with $50~{\rm fb}^{-1}$ of
LHCb and $50~{\rm ab}^{-1}$ of Belle-II data. We find that the Manohar-Wise
model could explain the current data, especially when the couplings of the
charged colour-octet scalars to quarks are complex, with the resulting
$\chi^2_{\rm min}$ being significantly smaller than that of the SM. Finally, we
investigate correlations among the two isospin asymmetries $\Delta(K^*\gamma)$
and $\Delta(\rho\gamma)$, as well as the averaged time-integrated branching
ratios $\bar{{\mathcal B}}(B_{s,d}\to \mu^+\mu^-)$; some of them are found to
be quite strong and could, therefore, provide further insights into the model,
once more precise experimental measurements and theoretical predictions for
these observables are available in the future.
