10/16 Bounties: 5 of the 6 can be done on Earth:

Bounty	Description	Hints
Relic Harvest	Cosmodrome Collect 200 Sensor Mites in Cosmodrome	Defeat enemies at the Cosmodrome (obvious) which can be done while you're picking up the rest of these.
One For All	Achieve Gold Tier Rating in Public Events	This can technically be done anywhere, but I personally think that the Cosmodrome has the most easily available Public Events.
Exalted Hive	Kill 10 Hive Majors or Ultras	Just to the left of the spawn point in the Cosmodrome, there is a building near the mission beacon. Go down the stairs and around to the right to find 3 hive majors that will re-spawn whenever you go all the way back upstairs and wait half a minute. (You could kill the Shank and other enemies that appear while you're up there for extra Mites if you wanted.)
Overcharge	Kill 2 enemies at once with a Fusion Rifle, 20 times.	Again, this can technically be done anywhere, but if you're already at the Cosmodrome...
Patrol Cosmodrome	Complete 6 Patrol missions in the Cosmodrome	Again, obvious. Pick up missions anywhere in the Cosmodrome (though I recommend just the open ghost, triangle, and target ones as the former really only involve killing things and the target gives you more rep than any other patrol mission).

Kill 10 Cabal Ultra/Major

First thing you want to do is head to Mars (obviously) and go to Exclusion Zone, which is the very first Story mission (Level 15) on Mars. Make sure you set the difficulty to a Heroic Modifier, or it will not work.

Once you zone in, Dinklebot will tell you that he has to link your sparrow to the planet. Once he hits the Cabal failsafe and the Cabal starts flooding in, you will start killing them off. When the 2nd drop ship comes in, it will drop 9 Cabal Majors. Focus fire only the majors and keep a few red health mobs up so they can kill you. Wash and repeat once and bounty complete.

After you respawn, you will have to start from where Dink-bot hits the failsafe once more, so you will have to deal with the initial mobs from the beginning.

Huge Reddit thread with info:

Bounty Masterpost