This paper investigates the stability of perturbations near equilibrium states for the two-dimensional Boussinesq-magnetohydrodynamics(MHD) system with fractional horizontal dissipation in the domain Ω=T×R, where T=[0 ,1] is the one-dimensional periodic box. The absence of vertical dissipation, combined with the presence of fractional operators, presents significant challenges to the study of stability and long-time dynamics in the Boussinesq-MHD system. To address these issues, we leverage the orthogonal decomposition method in conjunction with multiple fractional anisotropic interpolation inequalities and a fractional Poincaré-type inequality within our analytical framework. We prove the global stability of the system when the initial data are sufficiently small in H 2 ( Ω ) . Moreover, as time tends to infinity, the oscillatory part of the solution converges exponentially to zero in H 1 ( Ω ) .