No, the handgun ban is not a reasonable restriction on the right to bear arms, because the constitution did not say anything about reducing the right to bear arms to only certain types of arms. The handgun ban in DC is unfair, because guns should only be taken away from criminals, not law abiding people.
Part of the Second Amendment right to bear arms includes the right of armed self defense. For many people, especially those in heavily urban areas, hand guns represent the most efficient and effective self defense weapon is a hand gun. Banning handguns therefore effectively denies citizens that right to armed self defense.