Copyright only exists up to 70 years after the author's death. Seeing as most of the people who wrote the Bible are somewhat older than that, I can't see it being a problem.
Yes, just make sure you're using a translation which is out of copyright - which basically means King James's Authorised Version. The Revised Standard Version looks the same and isn't - tidied up, sanitised I think Victiorian - so may also be out of copyright. Any other translation and you could be in trouble...
Emma
<Added>
Of course, which version you use could be a nice little character point...
What about the view that the Bible represents the mediated word of God? Entertaining pictures come to mind of intellectual property lawyers debating in court whether God has been dead for 70 years or not.
(Apologies to anyone with religious sensibilities whom I might be offending...)