Where is the prayer of salvation located in the Bible?

Answer 1

It's not. There is no Biblical record of such a practice ever being taught or practiced.

The "prayer of salvation" practice originated in the Reformed theology of Huldreich Zwingli, ca. AD 1523-1525. Ironically, even though Zwingli introduced the practice, he probably didn't subscribe to it himself. In Reformed theology such a prayer would be seen as a "work of man" whereas salvation is seen as an election of God alone. (This theological system also reads a lot into the scriptures!)