After the bromonium ion is formed, there is a positive formal charge on the bromine atom. Consequently, the bromine atom essentially behaves as a protonated oxygen atom when we perform acid-catalysed ring opening.
So, the attack on bromonium ion ring would be like that of acid-catalysed epoxide opening, hence MeOH shall attack the site where the positive charge is stable. This site seems to be the one near the lone pair of oxygen atom rather than near the π-bond as that bond would be polarised to a high extent due to ketonic group.
In such reactions of bromonium always the $\mathrm{S_N1}$ path which you say is preferred, even though it’s not strictly $\mathrm{S_N1}.$ Rather, it should be called $\mathrm{S_N1}$-like.
Hence the answer seems to be option (ba).