Writing this now so I can either be supremely smarmy about it if I'm right, or I can laugh at myself horribly if I'm wrong.
Mind you, I hate overly ambitious fan theories in New Whom because they really ruined my appreciation for the product that ended up on screen, especially in the RTD years. Gallifrey Base was full of insane, mind-blowing theories like "The Master is hiding in Harriet Jones' clock" and used the 4-tone signaling system as proof of his influence over her, or "Harriet got turned into the Red Dalek" that I was expecting something, anything mental to happen in the resolving episode, and when it didn't, I would be (irrationally) upset because I'd mentally set expectations so high.
(I still think that RTD's setup episodes were epic but wrote cheques the payoff episodes could not cash but that's a rant for another time.)
Anyway, that all being said, I still do have THOUGHTS and SPECULATIONS.
Bill as Susan. (Mind you I'd thought Clara could have been Susan, too, but it looks like she was EVERY companion at some point-- maybe she was even Turlough, lol)
Why do I think this?
First, the obvious misdirect: When she comes into the Doctor's office, he's got a picture of Susan prominent on her desk.
Second, she's got vague memories of her mother, for whom strangely no photos exist until the Doctor gets her some by going back in time. This could be a possible fobwatched fake / lack of memory and the Doctor just picking some random person's photo to "be" her mom.
Third, she doesn't seem to bat an eye at the Doctor being in the Photos, or at the mysterious vault. Like she already subconsciously "knows" this is "normal" or has an induced blind spot
Fourth, she's very keen and perceptive, like Susan was. (Obviously that is a common-ish trait, but add to the overall pile of instances and it may be relevant)
Fifth, the lines about the Doctor being her dad / Granddad in a plot about family relations being confused by intentional deception and muddled memories.
Sixth, when Bill asks the Doctor about regeneration, he gets very uncomfortable. Is she a regenerated Susan and the knowledge of that plus that he can't reveal her identity to her makes him uncomfortable?
Problems with this theory:
1 - it's probably all rubbish caused by intentional misleading clues. (Probably most likely true, but that can be said of any fan theory, really)
2 - IIRC in the Audios which are semi-canonical thanks to "Night of the Doctor", Susan was killed off in the Time War, and the Doctor seems to have implied this again and again over the course of the series. EDIT: Apparently I do NOT recall correctly so she's still canonically possible. (BUT: It's a Time War, things shift and change all the time, and Gallifrey is back. What if the "fact" of her death changed? Or he was lying all the time and had her fobwatched and protected like the Master was, and deliberately forced himself to act as she was dead to keep her safe? --Not likely. When you start having to make convoluted explanations like that to make the theory work, s'probably not right)
3- It robs Bill of her own awesomeness - this is the bit that would hurt me if I was right. A person can be insightful and clever, and brave, all without being a member of (an admittedly awesome) alien race. And Billie has been one of the best companions of the modern era. To have all that be reduced to "oh, it's because she was Susan Foreman all along" would honestly suck.
Still. I'm throwing this out there so I can be all chuffed if somehow it turns out to be true, and if it's not, you can all just laugh at me~
Having successfully invaded both America and Canada from her home base in Windsor, Paisley has become horribly corrupted by the world. She hates active voice and wishes to god Twitter had an edit button. Dedicated to "creating the greatest 'Ship of them all", she ponders horribly terrible, idiotic things for your amusement.