Include a parenthetical reference to the version of the Bible you are using the first time you cite it in your paper. You only need to include this the first time; after that, it is assumed that you are referring to the same version of the Bible.
Write out the chapters, verses or lines you are using if you are referring to a specific part of the Bible. Include these in your parenthetical reference immediately before the version, or work them into the text if you prefer. The APA style blog provides an example for each of these options:
The Bible enumerates these virtues: “And now these three remain: faith, hope and love. But the greatest of these is love” (1 Cor. 13:1 New International Version).
In 1 Cor. 13:1 (New International Version), the Bible states that of the three virtues of love, faith, and hope, love is the greatest.
Leave the Bible out of your references list. This is one of the rare works that does not follow the typical APA style rule of including everything you cite in your reference list. Mentioning the version of the Bible in the text is considered enough identification.