Visibility:

You gain visibility by equipping a lightsaber, initiating combat with a lightsaber, and using any Jedi-related skills that consume Force power within range of other players or NPC's. You will gain a little at a time for using it in front of a few people. Do it in front of a lot of people (like in a starport) and you will almost immediately appear on the BH Terminals.
The range for visibility is 32 meters. Performing any of the above acts in front of PC/NPC’s within that range will increase your visibility.
It is unknown if you gain visibility for just having a lightsaber or robe equipped.
It is also unknown if you gain visibility only upon using a force power or if having a latent Force power active in front of others (such as Force Run or Force Armor) will gain you visibility as well.
It is rumoured that only NPC's that you can loot credits off of will count towards gaining visibility (but they all seem to drop credits now after publish 10.2).
The increase to a Jedi's Visibility Value (JVV) is determined as follows:
An opposing faction member who views this action will add the full value of the action to the Jedi Visibility Value.
A Neutral PC or non-animal NPC will increase the JVV by 50 percent of the action's Jedi Visibility Modifier.
A same-faction PC or non-animal NPC will increase the JVV by 25 percent of the action's Jedi Visibility Modifier.
Being grouped with a PC or non-animal NPC who is viewing this action has no influence on how Jedi Visibility is obtained. In other words, group members will still increase your visibility regardless.
Note that for Neutral Jedi everyone else is considered Neutral when calculating the increase to visibility. No one is considered to be of an allied or opposing faction and will always increase the JVV by 50 percent of the action’s Jedi Visibility Modifier.
Visibility decays over time, taking three weeks to decay fully.
Bounty Hunter Missions:

Once you have gained enough visibility you will appear on the Bounty Hunter Terminals, where any number of BH's can pick up the mission and try to hunt you down to kill you.
Bounty Hunters with a mission will gain a BH TEF that allows them (and anyone in their group if you attack back) to freely attack the Jedi that they have a mission for.
If the BH kills you he will complete the mission and receive the reward. Your Visibility should be reset after this.
If you kill the BH, then him and any other BH’s will fail the mission and lose the BH TEF on you. However, your Visibility will still remain the same though.
Jedi must deathblow BH’s in order to make them fail their mission.
There are currently many problems with BH Jedi Missions, such as everyone in a BH's group getting a TEF on a Jedi, the BH TEF not clearing after killing the Jedi, triple incapping a Jedi to avoid losing the BH TEF, and so on...