Damage Bonus starts at level 28 and rises from there. On 1 handers, it will scale to 13 at level 65 (about 1 every 3 levels.) 2handers will use a different formula based on the delay of the weapon.
Three things to note about damage bonuses. (Common misconceptions)
1) Damage bonus is based on the *character* not the weapon. All melee characters get a damage bonus when they hit 28.
2) Damage bonus is only used on the *primary* hand weapon. The offhand weapon (if dual weilding) gets no bonus, even though it will show.
3) Damage bonus is damage added *after* all other damage has been calculated. Thus, with a damage bonus of 1 in your primary hand, your minimum hit will be 2.