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.
I think this makes sense. In the episode Rose you see all those photos of Nine at the assassination of Kennedy and at the Titanic (on his own). But also in that episode he’s checking his reflection in the mirror like he’s seeing it for the first time, so he can’t have been long regenerated. So maybe he does all that stuff in the time before he comes back and says “Did I mention, it also travels in time?”
which makes that line even more powerful because this time he would really want her to say yes, because he knows what it’s like without her.
What’s interesting are the events the Doctor (theoretically) chose to visit during that time between when Rose (theoretically) first said no, and when he returned to extend the invitation a second time. Nine was photographed/drawn near the Titanic, Krakatoa, and the Kennedy assassination. All horrible catastrophes with tragic loss of life, all catastrophes that caused profound change in human history, catastrophes that (if Pompeii and Bowie Base One are anything to go by), would likely qualify as fixed points in time.
This leads me to believe that the Doctor was nearly in the throes a Time Lord Victorious breakdown as a result of the Time War and Rose’s rejection. He was dancing around the edges of these fixed points, likely looking for a way to save lives and prove to himself that he wasn’t a vile person. To prove to himself he could make a difference.
To prove to himself that he’s worthy of having someone brave and clever like Rose as a companion.
And Nine (obviously) doesn’t save Kennedy’s life or stop the eruption of Krakatoa, but in the episode “Rose” we find out he DOES save one family originally scheduled to travel on the Titanic by convincing them to delay their trip. A small measure of redemption.
Enough so that the Doctor summons the courage to return to that dark London sidewalk and casually lean out the door of his TARDIS like no time had passed at all, like he hadn’t been scrabbling in the wake of Rose’s rejection. And then he said the words he’d practiced alone in his console room dozens of times, with the exact amount of calculated swagger he’d rehearsed: “By the way, did I mention it also travels in time?”
