It has recently been pointed out that a component of the observed gamma-ray emission in the low latitudes of Fermi bubbles has a spectral shape that can be explained by a 10 GeV dark matter (DM) annihilating to tau leptons with a cross section of $2\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}27}\text{ }\text{ }{\mathrm{cm}}^{3}/\mathrm{s}$. Motivated by this possibility, we revisit the annihilation of a 10 GeV neutralino DM in the MSSM via stau exchange. The required stau masses and mixing, consistent with LEP direct search and electroweak precision constraints, are correlated with a possible enhancement of the Higgs decay rate to two photons. We also explore the implications of such a scenario for DM relic density and the muon anomalous magnetic moment, taking into account the recent ATLAS bounds on the chargino and the first two generation slepton masses, as well as the constraints on the Higgsino fraction of a 10 GeV neutralino.