Board Thread:Questions and Answers Forum/@comment-24901923-20141120150414/@comment-25250760-20141120190832

Your best bet for that stage of the weapon bounty is to keep checking the Gunsmith. Eventually, he will sell a rare fusion rifle.

This does not require you to be in game, as you can check vendor stocks using both the Destiny companion app and the Bungie.net website.

http://www.bungie.net/en/Legend/Tower/