Why is Leslie from Bridge to Terabithia so brave?

I would say that the text gives several good examples of Leslie being brave; however, the text does not offer much explanation as to why she is as brave as she is.  It could be a genetic trait, and she was simply born brave.  But I don't believe that a person is entirely determined by their genetic nature.  A person's environment plays a large role in shaping a person's behavior too.  This would be their nurture.  I believe that Leslie is brave because her parents have taught her to be brave.  Whether it was intentional or not is unknown, but Leslie's parents have a huge impact on her.  Both of Leslie's parents are well educated people.  Consequently, Leslie is a well educated young girl too.  That education builds self-confidence, and self-confidence often looks like (or is) bravery.  
Leslie's bravery might also be a coping mechanism to a new environment.  She has just been moved to a new city and a new school.  She's smart enough to know that if she wants to make friends, she is going to have to be brave and make an effort at it.  If she stands in the background of things, she might never make any new friends.  That could be why she gravitates to the running races in the first days of school.  She likes running, and she is good at running.   Those two things give her the bravery and the confidence to try and break into the recess races.  Her bravery works too.  It doesn't net her a lot of friends, but it nets her a wonderful friend in Jess.