We build a covariant holographic entanglement entropy prescription for a class of closed FRW cosmologies, generalizing a recent holographic proposal in de Sitter space. Starting from the Bousso covariant entropy bound, we describe the location of two holographic screens associated with a pair of antipodal observers, and then state our holographic proposal. We then apply our prescription to compute the entanglement entropy of the two-screen and the single screen systems, focusing on the leading classical contributions of order $(G\hbar)^{-1}$. First, we show how the full spacetime is expected to be holographically encoded on the two screens. Second, we argue that the exterior region between the two screens behaves as an Einstein-Rosen bridge, arising from the entanglement between the holographic degrees of freedom as suggested by the ER=EPR conjecture. The entanglement between the two screens, or from the geometric point of view the area of the minimal extremal surface, varies during the cosmological evolution, hence entailing a time-dependent ER=EPR realization.