First off let me say that the exotic weapons gained from the bounties aren't that great with the exception of Thorn & Invective. However if you are dying to get one you can try what I did. Complete 4 Vanguard bounties; it hasn't worked for me if I do Crucible or any other number of bounties. Go to turn them in but spam the button and turn them in at a very rapid pace. And that's it! This may sound stupid but just look at my profile and you will see the proof. I have Invective, Super Good Advice, Pocket Infinity (worst bounty to do, only finished because of the Treasure Cave), and I'm working on Bad JuJu. Also I had to abandon two other exotic bounties because they tend to offer the same ones. I also shared this with a friend and it worked for him on his first try. So to conclude, try it! What have you got to lose?
If it works for you let me know! Feedback is appreciated.
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I always complete the most bounties I can at once, and I've always spammed the A button to turn them in at a rapid pace. I usually only do the Vanguard bounties. I've gotten 8 Exotic Bounties since release. You might be on to something.