The Bible was the central book of several religions, most notably Christianity.
In 1605, the Doctor observed the translation of the Bible into the English language. (MA: The Plotters)
In 1609, Cardinal Robert Bellarmine used the Bible as a guideline while moderating the Armageddon Convention. (MA: The Empire of Glass)
In 1943, Reverend Wainwright tried to hold back attacking Haemovores with his faith in the Bible, but his faith was too weak and they overwhelmed him. (DW: The Curse of Fenric)
In 2003, an archaeological expedition used the Bible as a guide in their search for Noah's Ark. (NA: Eternity Weeps)
In 2008, Sarah Jane Smith quoted the Bible to Mrs Wormwood. (SJA: Invasion of the Bane)
Real world
As far as the Doctor's travels are concerned, the franchise has generally avoided making references to the Time Lord being present at, or involved in, any of the events featured or referenced in the Bible. A notable exception occurs in DW: Voyage of the Damned in which the Doctor claims that he took the last room at the inn in Bethlehem, which forced Joseph and Mary to find alternative accommodation. (The Doctor's purpose for being there is left unstated).
Another possible exception occurs in DW: Planet of the Dead, in which the Doctor claims he was present as "the original" Easter, though he is interrupted after saying "What really happened..." before he can specify whether he means the resurrection of Jesus (the event Easter commemorates), or the first formal celebration of Easter, and before he can elaborate further as "what really happened".