You can get a bounty if you kill another player in PvP combat or damage someone's C.A.M.P.
If you are Wanted, you are considered hostile to all other players, and they can strike you for full damage (as you can to them). You may be able to survive for a while, and the Caps reward (seen on your screen) increases each time you kill another human. The reward is also usually greater if the Wanted foe is a higher level than the hunter who tracks and slays them.
The only method to get rid of a bounty is to get killed by another player.
For more information on PvP interactions in Fallout 76, visit our help article here:How does player versus player (PvP) interaction work in Fallout 76?