We investigate the topological insulator state of gated bilayer silicene in the presence of extrinsic Rashba spin-orbit (SO) coupling. The system exhibits a band insulator (BI) phase for small Rashba SO coupling, and then translate to a strong topological insulator (TI) phase with both spin and valley filtered at large Rashba SO coupling. The strong TI phase is robust in the presence of intrinsic SO and intrinsic Rashba SO couplings. When a titled electric field is introduced, the in-plane component of the electric field gives rise to an interlayer Rashba SO coupling, and the system turns to a BI phase no matter how large the Rashab SO coupling and bias voltage are. This will provide potential application in nanoelectronics based on silicene.