When speaking of the Bible in Alcoholics Anonymous or Alcoholics Anonymous History, it is important to define the time and place involved.
Early Akron A.A.'s Christian Fellowship was founded in June, 1935. Its first group--Akron Number One--was founded July 4, 1935. In that period, Alcoholics Anonymous was Bible based in every respect. Dr. Bob said the oldtimers believed the answers to their problem were in the Bible. His wife Anne Smith said the Bible should be the main Source Book of all. She said not a day should pass without reading it. The Bible was read at meetings. Study of the Bible was stressed. And, when asked a question about the program, Dr. Bob usually replied: "What does it say in the Good Book?" And the three parts that were considered absolutely essential were: the Book of James, Jesus' Sermon on the Mount, and 1 Corinthians 13. In short, early A.A. was based on the Bible.
For sources of these ideas, see http://www.dickb.com/aa-bible-resources.shtml
For a line by line, verse by verse, comparison of A.A. language and the three segments--James, Jesus' Sermon, and 1 Corinthians 13, see Dick B., The James Club and the Original A.A. Programs Absolute Essentials. www.dickb.com/JamesClub.shtml.
In many parts of the country, many AAs continued to read the Bible, talk about the Bible, and quote the Bible. This was both before and after the Big Book and Twelve Steps were published in 1939. There are many quotes of Dr. Bob's statements about the Bible during the period and up to the point of his death.
On the other hand, when the Big Book was published in 1939, A.A. opened its doors to Christians, non-Christians, atheists, agnostics, people of many faiths, and people who believed in nothing at all.
This did not alter the fact that there were large number of Christians and Bible-readers. And that situation continues to this very moment.
The point is that the doors were opened. But they were not closed to Christians, those who studied the Bible, and those who continued to read Christian literature and devotionals.