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.