In my opinion, any large move to ban the Bible, whether as a cultural attitude of parenting or a enforcement by law would make the religious right movement grow in membership by bringing in the rather large moderate Christian contingent under the banner of persecution.
Popularizing such an attitude will only lead to more "In 20 years, only .000009 percent of the world will be Christian and thus the world will be swamped by atheistic, immoral rapists and murderers" type statistics and a resurgence in the whole "we are radical underdogs who will SPREAD THE FAITH. FAITH WARRIORS YEAH" scene's members.
Now on a personal level? I would ban biblical sermons and twisted forms of reasoning from my household, but not deprive any of my future children of their choice to read and consider any religious text in their purer forms. I think(and hope) by the time any of my future hypothetical children are old enough to be on a high enough reading level to read the Bible they will know enough about science, philosophy and history to read it with some healthy rational skepticism on their part, making any sort of guidance or input from me unnecessary.