I did each of Bitral and Elanye's tasks once, then repeated Gathering Silk, and my faction was good enough to start Tier 1 DoN progression. This is the text that appears when Bitral won't give you any more tasks:
Wayfarers Mercenary Bitral says "I understand your desire to win the hearts of Norrath's Keepers. I'm sure they'd be happy to talk with you."