I'm not sure why the quest for this excellent weapon doesn't show up on the quest page but I'll explain the start here.
I did the Barnett's Shield quest at Level 13 and got the Jagged Axe. At level 15, I went and talked to Bedalia to get the Bloody Sword quest but she wouldn't give it to me.
I eventually did Niea's Brother quest and the followup, Gleran's Necklace quest, and then returned to Bedalia and she gave me the Bloody Sword quest. Whew!
One hint for infiltrators and mercenaries: Once you get the sword, /broad in Camelot to buy another one. Most players will sell it cheap since it's relatively easy to get one (but not two). I actually got my second for free and am dual wielding them. Great weapons considering they are much higher DPS than the jagged axe.
DPS is 6.0 and getting two, +2 slash bonuses is very nice!