Bella never sings to Edward.
the song that Edward composed himself for Bella.
In the Twilight book series by Stephenie Meyer, Bella Swan's favorite song is "Flightless Bird, American Mouth" by Iron & Wine.
Bella's Lullaby by Carter Burwell
Bellas lullaby
Edward gave Bella a CD with the song he wrote for her recorded in it.
if you are talking about the song that edward plays for Bella it is called Bella's Lullaby and it is by Carter Burwell
the song that edward plays for Bella in twilight is called Bella's lullaby. he wrote it for her when they first met. its beautiful!!! actually there are several "Bella's lullabys" on this album..the name of the actual song is "kiss the rain" by yiruma the other "Bella's lullaby" is by carter burwell
the song that was playing while edward sucked the venom out of Bella's arm where James had bitten her was "LET ME SIGN"
its called " Who are They?"
If you are talking about the end of twilight, when edward is sucking the venom out of Bella's hand, the song playing is called, Let Me Sign, by Rob Pattinson.
If you mean the song Edward was listening to in his car, the song was Clair de Lune by Claude Debussy.