  In this paper, we propose a way to realize topological $s$-wave
superconductivity with application of circularly polarized laser light in
two-dimensional bilayer transition metal dichalcogenides (TMDs). Using Floquet
theory, we analyze a tight-binding model of bilayer TMDs with time-periodic
electric fields. After deriving an effective Hamiltonian, we investigate
topological properties of the $s$-wave superconducting state. The laser light
induces valley-dependent layer polarization and makes the system to be a
topologically nontrivial superconducting state characterized by the Chern
number. We show topological phase diagrams in the absence and presence of the
Kane-Mele spin-orbit coupling which causes hidden spin polarization in bilayer
TMDs. Although the topological phase diagram is affected by the spin-orbit
coupling, topological superconductivity can be realized without relying on the
spin-orbit coupling in sharp contrast to a previous proposal of laser-induced
topological superconductivity [K. Takasan, \textit{et al.}, Phys. Rev. B
\textbf{95}, 134508 (2017)]. We also discuss experimental setups to detect the
topological phase.
