When the Ninth Doctor first asked Rose to travel through time with him and refused, the Doctor accepted that and moved on. He traveled through space and time, saving the universe, all lonely for years thinking “I wish Rose could have been here.” Eventually, he goes back to a few seconds after he left Rose and says “By the way, did I mention it also travels in time?”
Rose never knew how long the Doctor waited for her.
WHY WHY WOULD YOU DO THAT
I think it’s more than headcanon — I think it’s actual canon, considering that earlier in the episode it’s established that:
a) At Rose’s apartment, he sees a reflection of his new appearance for the first time, implying that London 2005 is one of, if not the very first location he goes after regenerating; and
b) somehow the Doctor ALSO ended up dockside at the Titanic, at JFK’s shooting, and the explosion of Krakatoa without any companions in tow, according to the artwork/photos that Clive shows Rose.
How can both be true? Easy: After he leaves her with Mickey at the end of the episode, the Doctor takes a few solo pleasure strolls (to completely horrible historical tragedies best known for the senselessness of the losses of human life involved, of course) only to eventually find his way back to Rose’s side, a few seconds after he’d left.
Man, Season 1 of the Doctor Who reboot is so tightly written. Not a line out of place, not a wasted word or shot. I’ll grant you that Russell T. Davies went a little off the rails in Season 2, but man, Season 1 was just incredible, fucking incredible, a masterpiece of the small screen. /swoon