In this article, a statistical study on transverse permeability of random fibrous medium is performed. For that purpose, numerous random numerical microstructures are generated with constant or randomly varying fibre radii. Their statistical representativity with respect to experimental data is first briefly discussed. Flow simulations are then performed on these digital microstructures to retrieve their full transverse permeability tensor. The representative volume element (RVE) size is determined by studying convergence of permeability distribution when domain size increases. This allows to characterise the medium isotropy as well as the impact of geometrical randomness on permeability. The approach also integrates Gaussian process regression, that is a Bayesian machine-learning model, to consider variability within interpolation in the proposed permeability predictive model. In addition, this paper considers the impact of fluid slip at liquid/fibre interface on permeability for random fibrous media. An analytical expression is proposed to describe precisely the transition from a no-slip to a free-slip regime. This allows us to propose a probabilistic model that links permeability to both the fibre volume ratio and slip length. This finally yields two bounds for transverse permeability of fibrous media: a first related to statistical scattering and a second purely linked to fluid slip.