Localization of flux lines by columnar defects is investigated in the presence of point disorder. A (1+1)-dimensional model is analyzed in some detail. When point disorder is weak, the phase transition is found to be of the Bose-glass type. Some aspects of the Bose-glass phase itself may be marginally unstable to weak point disorder, but only beyond an astronomically large crossover scale. Correlated disorder is always irrelevant when point disorder is very strong. The Bose-glass transition is also studied in a small transverse magnetic field. Critical exponents for the commensurate-incommensurate transition that occurs in this case are derived using scaling arguments.