An ultrafast spin current can be induced by femtosecond laser excitation in a ferromagnetic (FM) thin film in contact with a nonmagnetic (NM) metal. The propagation of an ultrafast spin current into an NM metal has recently been found in experiments to generate transient spin accumulation. Unlike spin accumulation in equilibrium NM metals that occurs due to spin transport at the Fermi energy, transient spin accumulation involves highly nonequilibrium hot electrons well above the Fermi level. To date, the diffusion and dissipation of this transient spin accumulation has not been well studied. Using the superdiffusive spin transport model, we demonstrate how spin accumulation is generated in NM metals after laser excitation in an $\mathrm{FM}/\mathrm{NM}$ bilayer. The spin accumulation shows an exponential decay from the $\mathrm{FM}/\mathrm{NM}$ interface, with the decay length increasing to the maximum value and then decreasing until saturation. By analyzing the ultrafast dynamics of laser-excited hot electrons, the ``effective mean free path,'' which can be characterized by the averaged product of the group velocity and lifetime of hot electrons, is found to play a key role. The interface reflectivity modulates the spin accumulation near the $\mathrm{FM}/\mathrm{NM}$ interface and varies the spin decay length quantitatively.