Does anybody know the name of this song that plays throughout the scene? (See link)

This is not part of a song, this is just the music that will have been composed for that scene alone, there will be no more of it. However the song that plays at the end of this episode is callled When the pain dies down by Chris Stills. Sorry I couldn't help more!

Featured Songs - The Hero in the hold
    
Artist        
Chris Stills    

Song Title
When The Pain Dies Down    

Played When
closing scene

link

i'm not sure, but you could try tunefind.com or have-dog.com/bones

they always have the songs listed