A work that is in the Public Domain is not copyrighted. This is normally because the copyright expired, the work was created by an entity that is not eligible to claim a copyright, or the work was actively dedicated to the Public Domain by those who would have had the right to claim copyright. On some occasions, a work enters the Public Domain due to abandonment by the authors/translators and all of their heirs, usually when they had no intention of claiming copyright on the work in the first place. Public Domain status means that there are no legal restrictions on copying, publishing, or making derivative works due to human copyright law. Therefore, with a Public Domain Bible, you may freely copy, publish, distribute, print, adapt, make derivitive works (i.e. revisions and translations), sell (at cost or for profit), give away, broadcast, proclaim, preach, memorize, recite, incorporate in apps, and quote in other works in any amount, as much as you desire, for as long as you desire. You do not need to ask for permission to do any of these things, because there is no copyright owner with an exclusive legal right to control these uses. You may not claim a copyright on the Public Domain text yourself or prevent others from using the Public Domain text, even if you convert the text to another format. (Doing so is called copyfraud, and is a form of stealing intellectual property rights from the general public.) A Public Domain work remains in the Public Domain even if you print and sell it. You may, however, claim a copyright on your own creative works (such as study notes or commentaries) that you might publish along with a Public Domain Bible.
Bible translations that are in the Public Domain due to being dedicated to the Public Domain by those who worked on them include:
A Public Domain work may still have a translation name or other distinctive feature protected by Trademark law. In that case, the Trademark may only be used in accordance with the Tradmark owner's restrictions. In the case of the World English Bible and its derivatives, the Trademark may only be used to refer to faithful copies of the text as distributed from eBible.org.
Everything published before 1923 is in the Public Domain and not copyrighted. However, the King James (Authorised) Version of the Holy Bible is the subject of another form of restriction because of non-expiring Letters Patent granting exclusive printing rights for this one Bible translation and the Book of Common Prayer to a limited number of printers in England, Wales, and Northern Ireland, and only affect printing in those countries and import of printed King James Version Bibles and Books of Common Prayer into those countries. These have no effect in most of the world. King James made no mention of restrictions on electronic editions. As far as I know, no other Bible translation is subject to this sort of restriction.
Public Domain status does not expire. All copyrights expire, however, and the result when a copyright expires is that the formerly copyrighted work enters the Public Domain. The rules on when a copyright expires and the covered work enters the Public Domain are complex because of variations in laws between countries and changes in law over time. An authoritative summary for copyright expiration in the United States of America is in this circular by the United States Copyright Office. Another excellent reference on copyright expiration and the Public Domain is available from Cornell University.
God takes the integrity of His Word seriously:
You shall not add to the word which I command you, neither shall you take away from it, that you may keep the commandments of Yahweh your God which I command you.
—Deuteronomy 4:2
I testify to everyone who hears the words of the prophecy of this book, if anyone adds to them, may God add to him the plagues which are written in this book.
If anyone takes away from the words of the book of this prophecy, may God take away his part from the tree of life, and out of the holy city, which are written in this book.
—Revelation 22:18-19