This was a bug with patch 1.5. It miscalculated the intended damage in the display screen if the inventory. The bow actually delivered the correct damage to the enemy. This display error was fixed in 1.6.
That may not be accurate. See, e.g., http://www.gamesas.com/topic/1364580-did-bound-bow-get-massively-better-in-15/, in which Sandslice and others tested archery damage in 1.5. Their results indicated that damage in 1.5
was substantially increased vs. 1.4,
and there was a display bug that showed even higher damage than was actually being done. It worked like this:
Before 1.5 (and in 1.6, it looks like), the damage formula for archery was (Bow Base * Skill Bonus * Perk Bonus * Gear Bonus * Potion Bonus) + Arrow Damage
In 1.5, testing revealed the actual damage formula changed to (Bow Base + Arrow Damage) * Skill Bonus * Perk Bonus * Gear Bonus * Potion Bonus
In 1.5, the damage displayed in the tooltip added the arrow damage to the above total. So you were, in fact, doing less damage than the tooltip indicated, albeit not very much less, unless you had low skill/enchants/perks.
In 1.6, assuming they have reverted the damage calculation back to what it was before, you very definitely are doing less damage with archery than you were in 1.5. Depending on what mix of smithing, skill, perks, enchants, and arrows you were using, your damage could have gone down very significantly.
For example, if you are using the Mystic Bound Bow, with maxed skill and perks, and +180% damage from enchants, in 1.5 you did:
(24 bow + 24 arrow) * 1.5 skill * 2 perks * 2.8 enchants = 403 damage (427 displayed).
Before 1.5 (and now again in 1.6 apparently), with that same exact loadout, you instead do:
24 bow * 1.5 skill * 2 perks * 2.8 enchants + 24 arrow = 225 damage (225 displayed).
That is a massive, massive decrease. Certainly would be very noticeable, and would account for why tons of people have been reporting that their bow "feels" like it does a lot less damage in 1.6 than it used to in 1.5. Many of these have been http://www.gamesas.com/topic/1377474-bound-bow-nerfed-to-the-ground/page__p__20849886__hl__bound%20bow__fromsearch__1#entry20849886