For Those of you struggling to get this quest with multiple level 80s:
2 Things: Firstly, if you have already completed a bountiful delve and used a restored coffer key, it doesn't matter which character has completed that Delve.
Secondly: Check all of your max level characters, one of them may have the quest you are looking for. I found it on my first level 80 character.
I found that this quest was stuck on my first level 80 character. I abandoned it, and when I re-accepted it on the same character (My first 80), I got credit for the other Alt having already completed a bountiful delve.
For the record, after abandoning this quest, I did log on the alt that had completed a bountiful delve, however I found that this quest was not available. So, when I logged back onto my first level 80 and re-accepted the quest, the quest accepted that I had completed a bountiful delve and everything was cool and I got the mount.