I've become accustomed to archery and want a bow with a bit more style, if someone could give me the starting quest and location of quest-giver that'd be great, or, if I have to find it, possible locations would help too.
There are several ways to get the Daedric Bow, unfortunately none of them are from quests.
At level 46 and above Daedric Bows can be found random in chests and can be dropped after killing Revered and Legendary Dragons.
At level 47 and above Niranye in Windhelm(must be available as fence) and Tonilia in Riften sells Daedric Bows. At the Brood Cavern one can be found by a dead archer and one can also be found on the counter of Syndus' shop in The Ragged Flagon
Smithing - At the smithing level of 90 and the Daedric Smithing perk you can create a Daedric Bow at a forge of a Daedric Heart and three Ebony Ingots.
Atronach Forge - You can also create a Daedric Bow using the Atronach Forge. This requires a Sigil Stone, which can only be obtained via the Conjuration Ritual spell. You will also need one Daedra Heart, one Ebony Bow, one Centurion Dynamo Core and one empty or filled Black Soul Gem.
You can read more at the Elder Scrolls Wiki.
The best way to guarantee a daedric weapon is to forge it yourself. Of course, you will need the daedric smithing perk. The bow requires a daedra heart and three ebony to forge.
You can also drop a daedric weapon in random loot starting with the level 46.
Unenchanted Daedric Bows will begin to appear throughout Skyrim at level 46 and enchanted bows can be found at level 47, albeit very rarely. These locations include:
- Found as random loot in chests.
- Enchanted bows dropped as random loot by Revered or Legendary Dragons.
- Niranye in Windhelm often sells enchanted bows after level 47 once she is available as a fence.
- Tonilia in Riften often sells both unenchanted and enchanted bows after level 47.
- Brood Cavern, one by a dead Archer, available after level 47.
- An enchanted bow may be found on the counter in Syndus' shop in The Ragged Flagon after level 47.
Thanks to the Elder Scrolls wikia for the info.