Our scene opens in a room. It’s quite a lovely room. An office sort of room with a desk covered in books and various knickknacks. There’s some rugs on the floor, some photos on the walls. It looks like a very normal room one might expect a professor or such to use.
The door to this rather ordinary but lovely room opens and our old friend Nardole steps into the room and gestures for a young woman to enter. She’s rather ordinary also. Pretty, but ordinary. No words are spoken but one can hear a noticeable buzzing as Nardole moves. And the thunk of a bolt falling to the floor. It would seem this isn’t our old Nardole but a Nardole robot.
Left alone, our ordinary young woman first awkwardly sits in the chair positioned in front of the desk, then gets up and explores the room. Her eye is in particular drawn to the large cabinet in the corner. A cabinet in the form of a big blue police call box with an out of order sign hanging on the door. This would appear to be a room known to The Doctor. The photos of River Song and Susan, as well as the mug full of sonic screwdrivers, confirm that this is a Doctor zone. But where is the Doctor and why does this room exist.
As the woman takes her seat again, she reaches out in curiosity to the mug of what to her appear to be very odd pens. As she reaches for one, a blast of extremely loud electric guitar music comes from the adjoining room. Played, of course, by the Doctor. He enters the room and inquiries if the young woman is Bill Potts and why she’s been showing up to his lectures when she’s not a student. She babbles an answer about how she loves his lectures and some nervous nonsense about a pretty girl and free chips (fries for the Americans). Then she attempts to change the subject by asking about the call box. It’s a trick that only works for a moment as the Doctor asks again why she is coming to his lectures and mentions that he’s intrigued by the little detail that when she’s confused, Bill smiles (most people frown). This leads into an offer to tutor Bill even though she’s not a student. An offer that Bill accepts.
(Can I just drop an aside here about how much I love the opening credits. This version of the music might just be my favorite)
The Doctor proceeds to give a lecture on the nature of Time, intercut with images of Bill at work in the Canteen, working on homework, hanging at a local club. There she has a ‘cute meet’ moment with a girl with eyes that seem to literally glee and sparkle. And time, for a moment, seems to stand still.
The Doctor concludes his lecture with the classic “Time And Relative Dimension In Space”.
Cut to morning, maybe the next day, maybe days later. Bill is crossing the campus when she seems The Doctor and Nardole walking somewhere and decides to follow. That somewhere turns out to be a basement and inside overheards the pair debating about The Doctor tutoring Bill and “getting involved”. Bill spies them working on something and is almost caught. As she sneaks back out she wanders into the girl from the club. Bill tries to flirt and fails rather miserably. The mystery girl wants to show Bill something. And being naturally curious, Bill follows (a trait that in this universe isn’t always a good thing).
The something is a puddle but its not an ordinary puddle (big shock) and a mystery voice from the other side announces that the link has been established. That can not be good.
Christmas time comes and Bill brings The Doctor a rug as a gift. He has gotten her nothing and she brushes off her gift as just being something cheap. They open a couple of Christmas crackers and Bill drops the detail that her mother died when she was a baby. She mentions that she has no photos of her mother, who hated taking photos and mysteriously a box of photos is discovered in the back of a closet by her adopted mother. In one of the photos there is a mirror in the background and it catches a partial image of a man with grey hair taking the photo (yeah we know who that is an it seems the Bill at least suspects),
Bill happens upon the mystery star eyed girl, Heather, at the site of the never moving puddle. As she walks around the fence to join Heather we hear a splash and Heather seems to have vanished. Bill leaves without noticing that Heather is trapped in the puddle (said it wasn’t good didn’t I). Bill tells the Doctor about the weird puddle and he bolts out of his office to the puddle’s location. She follows and is perplexed by his very Doctor behavior (weird questions, jumping about randomly, lots of “yes” and “of course” and saying things like the water isn’t water). The Doctor sends Bill home and she has a very horror film sort of moment when her mother calls but she can hear someone apparently taking a bath. When Bill enters the bathroom the tub is wet but empty and there is no one in the shower, although it too is wet as if it was just used. Cue Bill seeing what appears to be Heather’s star eye in the drain, and Bill runs out and to the campus, presumably in search of the Doctor. She spots a very wet Heather, or at least Heather looking thing, in the dark. The Heather thing mimics Bill’s comments, drawing Bill in closer, before it attempts to lunge at her. Bill runs to The Doctor’s Office where the strange Heather thing turns into water to slip through the crack under the door and get inside.
The Doctor drags Bill into the Police Box and she gets her first look at the TARDIS. And has her first trip when the Doctor shifts the TARDIS (with the two of them and Nardole) to the odd location Bill found early. The location is some kind of vault and the Doctor questions if the thing might be looking for the vault. It turns out that they seem to be target and they jump again in the TARDIS, this time to Australia. Unfortunately its not far enough so the Doctor takes them to 3 million years in the future and the far side of the universe. While they are there, the Doctor and Nardole start to sort out that the water thing is a kind of living spaceship that needed a Pilot and it took Heather because of her deep desire to leave her home and her life. What they can’t figure out why the Thing keeps following them. Including to that planet.
This time The Doctor takes them to the past, well the past relative to where they were, and into a war zone. A war where one of the sides are Daleks. The Doctor tricks one of the Dalek into attacking the Heather Thing. But instead of being destroyed, the thing takes over the Dalek and destroys it.
Finally they sort out that the thing not only took Heather’s body it absorbed her mind and with it her last thought that she wouldn’t leave Bill behind. The Doctor wants Bill to release the Thing from Heather’s promise but before she does, Bill experiences a kind of mind meld with the Thing and has glimpses of the universe.
They return home and The Doctor attempts to wipe Bill’s memories. He argues with her that he’s undercover and no one can know about him, the TARDIS etc. Bill begs him to let her keep her memories at least for a few days, live in the excitement just a bit longer. Finally Bill relents but not before asking The Doctor to imagine that their positions were reversed. It’s that question that gives the Doctor pause and he throws Bill out before he changes his mind. But as Bill leaves the building, she finds The Doctor and the TARDIS waiting outside.