  A scaling theory of vortex motion in Bose glass superconductors with currents
parallel to the common direction of the magnetic field and columnar defects is
presented. Above the Bose-glass transition the longitudinal DC resistivity
$\rho_{||}(T)\sim (T-T_{BG})^{\nu' z'}$ vanishes much faster than the
corresponding transverse resistivity $\rho_{\perp}(T)\sim (T-T_{BG})^{\nu'
(z'-2)}$, thus {\it reversing} the usual anisotropy of electrical transport in
the normal state of layered superconductors. In the presence of a current $\bf
J$ at an angle $\theta_J$ with the common field and columnar defect axis, the
electric field angle $\theta_E$ approaches $\pi/2$ as $T\rightarrow T_{BG}^+$.
Scaling also predicts the behavior of penetration depths for the AC currents as
$T\rightarrow T_{BG}^-$, and implies a {\it jump discontinuity} at $T_{BG}$ in
the superfluid density describing transport parallel to the columns.
