Number of Exotic Bounties
Here is a list of each exotic bounty and it's reward. Note if you click on the bounty, it will tell you the steps required to complete it.
Shattered Memory Fragment, Reward: Pocket Infinity (Fusion Rifle)
A Dubious Task, Reward: Invective (Shotgun)
Toland’s Legacy, Reward: Bad Juju (Pulse Rifle)
A Voice in the Wilderness, Reward: Super Good Advice (Machine Gun)
An Unknown Patron, Reward: Fate of All Fools (Scout Rifle)
A Light in the Dark, Reward: Thorn (Hand Cannon)
That's a total of 6 exotic bounties that are known so far.