Bravery Bonus

The bravery bonus only applies for the first completion of a quest. Running the quest additional times will not affect the bravery bonus nor give the bonus experience points. Thus, after the first run, you may run the quest on any difficulty and it will not affect your bravery streak.

This is actually two additional bonuses awarded to players for playing quests repeatedly on hard or elite. The first one is the base bravery bonus for doing a quest elite the very first time you ever do it on that character. It is +20%. This is on top of your streak bonus. And on top of the (upcoming) +80% first time on elite bonus - which you get regardless if you ran normal/hard already, unlike the base bravery bonus.

The other bonus is the streak bonus, which is 5% on hard and 10% on elite and stacks up to 5 times to a maximum of +25% for hard, and +50% for elite.

So it starts out at +100%, and eventually can reach +150%, if you only run elite.

In order for the bravery bonus to apply, your character level cannot be greater than 2 levels above the base level of the quest, e.g. if the quest is level 10 and you run it on elite your character level can be no higher than 12 for the bravery bonus to apply.

Power leveling penalties and restrictions may apply regarding getting these bonuses. Still to be confirmed, but apparently if any one of your party is over 2 levels above normal quest level, it counts as power leveling for the purpose of the bravery bonus and the bravery bonus won't apply. Was in a level 11 quest and when first entering said bravery bonus was in effect, but added a level 14 in middle of quest and at end was not awarded bravery bonus. Could be that re-entry caused a loss of bonus.

External Links:
 * Bravery Bonus (BB) and You!