“It’s the oldest story in the universe, this one or any other. Girl and girl fall in love, get separated by events. War, politics, accidents in time. She’s thrown out of the hex, or she’s thrown into it. Since then, they’ve been yearning for each other across time and space, across dimensions.
This isn’t a ghost story, it’s a love story!”
The fundamental misunderstanding of the state in which Heather exists in after she becomes ‘the pilot’ is what drives the conflict in this episode, but it’s made abundantly clear that she is not dead.
When they meet in the park outside the Doctor’s study, Bill, seeing her in this new form, mutters “you’re dead!”, which is repeated back to her by Heather’s mimicry - the clear intention here (supported by Lawrence Gough’s brilliant directing style) being to establish the misunderstanding of her being ‘the monster’ while playing it off as a ‘horror’ moment. But, in classic Moffat fashion, the entire point of this episode is to subvert that idea.
I really have to praise Stephanie Hyam’s performance here because it’s key to understanding that Heather’s pursuit of Bill across time and space was something that she was directing. Notice how much emotion appears on Heather’s face whenever she catches up to Bill - she looks extremely sad when she appears in the Doctor’s study (see the fourth image above) and Bill gets in the TARDIS because that’s exactly why she’s here… to fulfill her promise to Bill that she won’t leave without her.
She appears positively elated to see Bill when they travel several million years into the future and cross to the other side of the universe, as her face emerges out of the water. There’s multiple occasions where Bill has a flashback to their time together earlier in the episode and we’re meant to think that it’s her remembering the girl that was before she became this creature, playing to a rather typical trope in how horror films are directed. But it’s actually establishing the opposite, as Bill slowly pieces together the reason why this is happening and realises that this has been Heather all along.
Perhaps the most obvious clue is given to us in how Heather assumes the form of a Dalek that’s trying to kill the Doctor. A Dalek! The Doctor wonders why she didn’t fire on them. She had a gun, after all - “the deadliest fire in the universe”, a Dalek’s weapon.
But she doesn’t use it…
Face-to-face, at last, she affirms her feelings towards Bill when she’s told “I really liked you”. Hyam’s performance here is just brilliant because she’s obviously having to mimic what Bill says, but you can distinctly hear the tone of sadness in her voice as she says the line back to her because this is where they part ways.
And she extends another offer to Bill, showing her what she’s become - how she sees the universe differently now, and all of time and space. And Bill is enraptured with it, but releases Heather from her promise because she’s (naturally) scared. Things still aren’t totally clear: she doesn’t know or understand what she’ll become if she accepts this offer because Heather isn’t totally human any more, but, as we’ve seen time and time again throughout the episode, right up to this moment, she’s still Heather.
The end of The Pilot has two rather important moments regarding the episode’s narrative arc with Heather. Back in the Doctor’s study, Bill asks if she’ll ever see Heather again, to which the Doctor rather cynically responds “I don’t see how”.
But, after Bill calls him out on the mind wipe situation and he’s reminded of Clara - who he’s very clearly still yearning to find - he shows up outside the university in the TARDIS and tells Bill:
“It’s a big universe. Perhaps, one day, we’ll find her…”
I can’t for the life of me find the quote, but, some months ago, Moffat said that there’s a very particular story they have in-mind to tell with Bill. I definitely don’t want Pearl to leave after one series, but it seems like a distinct possibility with the handover to Chibnall ushering in the next era of the show…
As such, I can sort of see how Bill’s story could potentially end if she’s only going to be in Series 10 and won’t carry over into the Chibnall era.
Similar to how Clara and Ashildr ended up with their own TARDIS and went off together to travel in time and space, Heather has her own time travel capabilities and Bill is clearly hoping that, in travelling with the Doctor, they will find each other again.
Naturally, that sets the stage nicely for Bill to continue travelling after her time as the companion is done with her new cosmic girlfriend.