I don't know if there is a specific answer for this question. There are several references to the Bible throughout Ray Bradbury's Fahrenheit 451.
Perhaps the reason Bradbury chooses the Bible is that it offers insight into the past, stories of people who were sorely tested, and guidelines to follow in order to survive. It may be that Montag's society is so lost that when the bombs fall at the end of the story, whatever Montag has read will help him and others rebuild. The Bible is full of advice, and provides direction for moral and ethical enrichment. Certainly a new society would need guidelines to rebuild and improve over mistakes made in the past.
Montag refers to Job at one point in the story, references are made to Caanan; at the end, Montag tries to recall parts of Ecclesiastes and Revelation.
Revelation deals with the end of times; perhaps Montag does not recall this as quickly as he might because they are preparing to start a new life (—those who have escaped what has been destroyed by the government). Ecclesiastes is a somber book. Its author:
Qohelet clearly endorses wisdom as a means for a well-lived earthly life...
This may reflect Bradbury's sense that with the end of civilization as they know it, these men can rebuild with caution and knowledge. Ecclesiastes also means "assembly." Perhaps the significance of Montag's reference to this book of the Bible refers to the "assembly" of survivors who will change the world for the better.
The Bible seems to be a book with a wide variety of knowledge and guidance. Montage needs this personally; the society will need this to rebuild.
I believe, the most accurate answer to that question is because Bradbury is a devout Christian. Look him up in Wikipedia.