  We study the band structure of phases induced by depositing bilayer graphene
on a transition metal dichalcogenide monolayer. Tight-binding and low-energy
effective Hamiltonian calculations show that it is possible to induce
topologically nontrivial phases that should exhibit spin Hall effect in these
systems. We classify bulk insulating phases through calculation of the Z$_2$
invariant, which unequivocally identifies the topology of the structure. The
study of these and similar hybrid systems under applied gate voltage opens the
possibility for tunable topological structures in real experimental systems.
