The optical response of layered transition metal dichalcogenides (TMDCs) exhibits remarkable excitonic properties which are important from both fundamental and device application viewpoints. One of these phenomena is the observation of intralayer/interlayer excitons. While much effort has been done to characterize excitons in monolayer TMDCs and their heterostructures, a quite limited number of works have addressed the exciton spectra of their bulk counterparts. In this work, we employ ab initio many-body perturbation calculations to investigate the exciton dynamics and spectra of bulk 2H-MX2 (M = Mo, W, and X = S, Se). For molybdenum-based systems, we find the presence of interlayer excitons at energies higher than the first bright exciton (XA), with non-negligible strength intensity. Our results also show that interlayer excitons in tungsten-based systems are almost degenerate in energy with XA and possess very small oscillator strengths when compared with molybdenum-based systems. At room temperature, and considering the thermal exciton fine-structure population for the XA-exciton, we estimate effective radiative lifetimes in the range of ∼4-14 ns. For higher energy excitons we predict longer effective lifetimes of tens of nanoseconds.