Yeah … what he said. :)
I would add that the Greek root Glenn refers to is biblion. There's also the Latin biblia. See the etymology here: http://www.etymonline.com/index.php?term=bible
The pronunciation of any Anglicized derivatives defaults to the usual pronunciation rules. Hence the long "I" in Bible and short "I" in bibliography. Same thing happens with natal and nativity.
What he said.
Further, the current pronunciation rules stem from some historical vowel shifts (see The Great Vowel Shift Harvard: Vowels) that depended upon the original vowel and some other phonetic context cues. One of the context cues was the stress patterns within the word, and how certain vowels fell in relationship to the stress. So stressed vowels tend to be pronounced "long" in modern English, and unstressed vowels tend to be "short" or even further reduced to indistinct articulation (schwa) or silent.
In this case, the i of Bible is stressed, so it is pronounced as long i dipthong. The i of bibliography is far before the stress, and is pronounced as short i.