After joining any Knightly Order and having a high amount of reputation, this quest can become available.
Accept the offer to receive an "ancient artifact of power" from a member of the order. Go to the dungeon mentioned by the employer and speak to the witch. She will ask the Agent of Daggerfall to kidnap her great granddaughter and, upon returning to her, she will then guide them to a dungeon containing either the bow, Auriel's Shield or the Lord's Mail.
Upon progressing through Nocturnal's quest and confronting the Battlemage, there is an alternative to accept the mage's offer and retrieve Auriel's Bow from a location he gives. If the bow is already obtained it cannot be received again, so instead he will offer the Warlock's Ring.