You can get Reins of the Grey Riding Camel by finding a Mysterious Camel Figurine.
Most of the time, these figurines turn into dust, but there is a small chance that it will teleport you to Dormus the Camel-Hoarder who drops the mount.
Make sure you are located in the old Uldum and not the BFA version. This can be changed by talking to Zidormi.
This requires: HandyNotes
If you use Routes, you can use this route to have a highlighted route to follow.