We study the ground-state and low-energy excitations of vortices pinned to columnar defects in superconductors, taking into account the long-range interaction between the fluxons. We consider the ``underfilled'' situation in the Bose glass phase, where each flux line is attached to one of the defects, while some pins remain unoccupied. By exploiting an analogy with disordered semiconductors, we calculate the spatial configurations in the ground state, as well as the distribution of pinning energies, using a zero-temperature Monte Carlo algorithm minimizing the total energy with respect to all possible one-vortex transfers. Intervortex repulsion leads to strong correlations whenever the London penetration depth exceeds the fluxon spacing. A pronounced peak appears in the static structure factor S(q) for low filling fractions f<=0.3. Interactions lead to a broad Coulomb gap in the distribution of pinning energies g(ɛ) near the chemical potential μ, separating the occupied and empty pins. The vanishing of g(ɛ) at μ leads to a considerable reduction of variable-range-hopping vortex transport by correlated flux-line pinning.