When does the Bible come up in "Miss Bernard said"?
The Bible does come up at least once in the manga. There is a two-page segment in volume 1, chapter 4 (p. 35-36), titled "The Bible said" (「聖書曰く」). It's kinda loony, like everything else in Miss Bernard said.




Page 35


  Panel 1
  NARRATION: Miss Bernard, a.k.a. Machida Sawako, was reading in the library, as was her habit. World-Famous Adages You'll Love to Use was one of her favorites.
  
  Panel 2
  SAWAKO: Hmm.
  NARRATION: What was Miss 'ard planning to do with these adages?
  
  Panel 3
  SAWAKO: When aliens attack and bring about the end of the world, I want to murmur a verse from the Bible as I stand there petrified... but I can't find anything suitable in here.
  
  Panel 4
  SAWAKO: Like, "the scales fell from my eyes" is apparently from the New Testament, but that's so lame.
  
  Panel 5
  VOICE: Aliens have attacked! The end of the world is nigh!
  
  Panel 6
  SAWAKO: The scales have fallen from my eyes... I guess?


Page 36


  Panel 1
  SAWAKO: Argh! This is no good! I need something more... Apocalyptic...
  
  Panel 2
  BIBLE: And the great city was divided into three parts, and the cities of the nations fell: and great Babylon came in remembrance before God, to give unto her the cup of the wine of the fierceness of his wrath. [...] and men blasphemed God because of the plague of the hail; for the plague thereof was exceeding great.
  
  Panel 3
  ENDOU: Revelation, chapter 16...
  
  Panel 4
  SAWAKO: That's too long! I'm not feeling it!!
  
  Panel 5
  SAWAKO: Oh. I found something good.
  
  Panel 6
  SAWAKO: When the aliens eat us, I'll say this verse!
  ENDOU: Them eating us is a done deal?
  
  Panel 7
  SAWAKO: Except a corn of wheat fall into the ground and die, it abideth alone: but if it die, it bringeth forth much fruit.


There may be other references to the Bible (I haven't read much past this chapter). If I do run into any more, I'll try to remember to update this answer.