In this note we establidh a relation between the Kobayashi relative intrinsic pseudo distance of a holomorphi fiber bundle and the one in its base. Moreover, we prove that if $(\widetilde{Z},\pi,Z)$ is a fiber bundle with compact hyperbolic fiber and $M\subset Z$ with $d_{M,Z}$ induces the given topology on $\overline{M}$, then $M$ is hyperbolically imbedded in $Z$ if and only if $\widetilde{Y}=\pi^{-1}(Y)$ is hyperbolically imbedded in $\widetilde{Z}$.