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In transition metal dichalcogenides (TMDs), the electronic band structure shifts dramatically when the thickness of a sample is reduced from bilayer to monolayer, producing a concurrent change in their optical properties. Exciton resonances form at the K points on the Brillouin zone boundary in both the monolayers and bilayers, however, we find that their quantum dynamics differ drastically. We perform two-dimensional electronic coherent spectroscopy (2DECS) on a MoSe₂ monolayer and bilayer to investigate the quantum decoherence (homogeneous linewidth) of various exciton resonances. We first identify the A-exciton and trion resonances in the monolayer. The bilayer A-exciton is shifted to lower energy, consistent with previous studies. Despite the presence of an inhomogeneous broadening, we were able to extract the homogeneous linewidth using 2DECS. Most notably, the homogeneous linewidth of the bilayer exciton exceeds that of the monolayer exciton and trion significantly. Because the band structure of a MoSe₂ bilayer evolves to an indirect bandgap, we expect that scattering with additional interlayer phonon modes would lead to additional dephasing, consistent with the increased homogeneous linewidths observed.