Using bus waveguides coupled to the graphene-loaded Si-ring resonators (GSRRs) all on a Si-‎on-insulator substrate, we propose a compact bidirectional switchable beam splitter/filter ‎controlled by graphene-based electro-absorptive (refractive) mode modulation. The proposed ‎device consists of a through waveguide coupled to two drop waveguides via two GSRRs. ‎Each GSRR consists of a stack of hBN/graphene/hBN nanolayers sandwiched between two ‎Si-ring resonators. Using a finite difference time domain method, we show that the resonant ‎wavelength of GSRRs can be tuned in the range of 1551.5 < λ <1552.1 nm, linearly with the ‎slope of ~2.46 nm/eV via appropriately changing the graphene chemical potential, ‎electrostatically. The numerical results show that when both GSRRs are in an electro-refractive ‎state and a transverse electric (TE) polarized light beam of an appropriate wavelength is ‎launched into one of the though-ports, ~ 84.5% of the input intensity equally splits between ‎the adjacent drop-ports. The transmission out of the second through-port is less than 0.8%. ‎The numerical results further show that when one GSRR is in an electro-refractive mode, and ‎the other one is in an electro-absorptive state, ~68.4% of the input intensity transmits out of ‎the drop-port adjacent to the former GSRR, and the other ports experience insignificant ‎outputs (<0.7%). The device's structural symmetry makes it a bidirectional tunable, suitable for ‎long-haul optical telecommunication applications.‎