- You may be looking for the person this construct is based on.
She existed in a Shadow World as a virtual replica of the original Bill from the Doctor's World. Like the rest of the Shadow World, she was created by the Monks, so that they could plan the perfect invasion of Earth.
Bill shared the history and personality of her non-virtual counterpart, only parting with that history shortly after the events aboard Chasm Forge. She was a perfect duplicate and, like the rest of the people living within the Shadow World, she believed herself to be real.
In the Shadow World, a virtual reality simulation of Earth, Bill's date with Penny was interrupted when the Doctor arrived and the Pope walked into the flat. Bill accompanied the Doctor and Nardole to the Vatican to read the Veritas, which had caused a number of devout Catholic priests to commit suicide. When a priest, armed with a gun fired a shot, Bill and Nardole left to investigate on the instructions of the Doctor before going through a portal that appeared in the wall.
They entered a white walled room with projectors projecting portals and entered one leading to the Pentagon and another that led them to CERN where scientists who had read the Veritas sent via email were planning to blow themselves up. When Bill demanded to know why they were doing it, one of the scientists had her and Nardole say any number they wanted when he hit the table. They both said the same number. This repeated with the scientist and eventually the whole room joining in.
Bill and Nardole, frightened by the experience quickly left before the dynamite wired to the canteen tables exploded. Nardole deduced that the projectors were actually projecting the locations not portals and stepped out of the light reducing to Computer code. Bill followed the blood splatters on the floor through another portal arriving at the White House where the Doctor had listened to the audio recording of the Veritas.
He explained to her that a demon that wanted to conquer Earth had made a shadow world to practice conquering and that aliens had done the same to practise conquering the planet in the present day. The Shadow Test was designed to help creatures living in either world work out whether they were in the real world or the shadow one. By getting the same numbers, Nardole and the Doctor had worked out they were not real and a part of the Shadow World.