•Model. We have introduced the 4-level cold Rydberg atomic system with the moiré lattices.•Method. The stationary solutions of different types are obtained through the modified squared-operator iteration method.•The system’s bandgap spectrum was obtained, and LBs are produced in the form of GSs.•Stable LB families of the fundamental, dipole, quadruple, and vortex types are produced.•Stability regions were investigated by means of the anti-VK criterion and linear stability analysis. Rydberg electromagnetically-induced transparency has been widely studied as a medium supporting light propagation under the action of nonlocal nonlinearities. Recently, optical potentials based on moiré lattices (MLs) were introduced for exploring unconventional physical states. Here, we predict a possibility of creating fully three-dimensional (3D) light bullets (LBs) in cold Rydberg gases under the action of ML potentials. The nonlinearity includes local self-defocusing and long-range focusing terms, the latter one induced by the Rydberg-Rydberg interaction. We produce zero-vorticity LB families of the fundamental, dipole, and quadrupole types, as well as vortex LBs. They all are gap solitons populating finite bandgaps of the underlying ML spectrum. Stable subfamilies are identified utilizing the combination of the anti-Vakhitov-Kolokolov criterion, computation of eigenvalues for small perturbations, and direct simulations.