So I have this theory:
When Rose said “no” to the Doctor on ‘Rose’ episode he came back to the Rose’s past to know a little about her, so he discovered TARDIS took him to the Christmas when she was 12. He found her with Jackie and Rose was asking her a red bicycle and a proper Christmas, but Jackie didn’t have money so she said they can’t, Rose was sad but she said “okay”.
At night Rose slept on sofa and that’s when Nine furtively get in and give her that red bicycle when she’s 12 he mentioned on ‘The Doctor Dances’.
When Ten lost Rose and couldn’t say he loves her and after he left Donna with her family, Ten came back to that night Christmas when his previosly form gave Rose her bicycle and when he saw himself go away he get in and put a blanket on her and he just stare to her for a while and before he go away, Ten just kiss her head and said what he couldn’t say in her future.
And one day when Eleven was saying goodbye to people he knows, TARDIS just lead him at that Christmas night he already was twice, and he just observe Nine and Ten go away, so he look at the room and resolves decorate it with a proper Christmas tree and stuff as Rose wanted early that day. It’s his last present to his pink and yellow girl.
So when Rose woke up at morning she noticed not only someone put a blanket on her at night but she got that shine red bicycle she asked to her mother and there was not only a Christmas tree but the room was proper decorate it. So when Rose standed up to touch the bicycle she found a Christmas card with just one word three times with tree different handwritings: “Thank you”.