Bounties come in 2 forms (Versus, and Horde). They can be found under the "Manage Bounties" tab after selecting either Versus or Horde game modes. To select a bounty press
on the card you want, you will see a "red check mark" showing it is selected.
Some bounties only count in certain Versus matches (ex. get 1500 score in King of the Hill) so make sure your playing the correct match type.
After you run out of your free Bounties more can be bought in the store through Gear Packs. You may also create Bounties for 40 scrap by deleting duplicate cards or unwanted cards by pressing
on the desired card. Hope this helps, and if you have any questions feel free to ask!