Should I capitalize "bible" in "the Christian Bible"? "the Discordian Bible"?
Solution 1:
The Christian Bible is two separate capitalization issues. The adjective Christian and the name of the holy document, the Bible. By convention, this text is not put in italics, nor are any of its books. The Book of Job, for instance.
The Hebrew Bible would be up for interpretation because Jews do not refer to their document as such. The Torah is clearly capitalized, as is The Five Books of Moses. I wrote a religious drama a while back and was not corrected for using lower case b in this particular example.
The Vatican Press does not capitalize he or him when referring to God, Jesus, or the Holy Spirit. Writers at this point should be cognizant of convention in their audience. Holy Communion, stations of the cross, Mass, Confession, the Sh'ma, and the Last Supper are some more examples.
Solution 2:
Yes - "Christian Bible" should be capitalised. Because the Bible is the name of a book - i.e. its title - it is a proper noun. However, "bible" can, as you mentioned, be used as a noun. In that sort of a situation it is not the name of a book but rather a "description" of it, thus it not requiring a capital letter.
"Bible" may also be capitalised as a sign of respect for God and Jesus, similar to the way some sources will capitalise "him" when referring to God. This, however, has been a question of style ever since the presence of the Bible due to the lack of capital letters in the Hebrew language.
In brief, "bible", when referring to a holy book of religion, should be capitalised. When "bible" is referring to a book of great usefulness, it is not capitalised.
Solution 3:
Nouns concerning religion are capitalized, especially words for God, the names of religions and their adjectives: the Lord, the Almighty, Paradise,the Bible, Christianity, a Christian, Protestanism, a Protestant service, a Roman Catholic church (source: my old school grammar).
There are a lot of web-sites about capital letters on the Internet, but words concerning religion are mostly forgotten. Nothing is perfect.