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We investigate the bounce realization in the framework of generalizedmodified gravities arising from Finsler and Finsler-like geometries. Inparticular, the richer intrinsic geometrical structure is reflected in theappearance of extra degrees of freedom in the Friedmann equations that candrive the bounce. We examine various Finsler and Finsler-like constructions. Inthe cases of general very special relativity as well as of Finsler-like gravityon the tangent bundle we show that a bounce cannot be easily obtained. However,in the Finsler-Randers space the induced scalar anisotropy can fulfill thebounce conditions and bouncing solutions are easily obtained. Finally, for thegeneral class of theories that include a nonlinear connection a new scalarfield is induced, leading to a scalar-tensor structure that can easily drive abounce. These features reveal the capabilities of Finsler and Finsler-likegeometries.

Bounce cosmology in generalized modified gravities