I really like the idea that the Curator was just the Moment in another guise. It had to go somewhere after the Doctors decided not to use it. Safest place would be in the Tardis. And it chose Rose/Bad Wolf because of how important and crucial she was to the Doctor after the war. I could see it taking on the appearance of one of the older incarnations, back when the Doctor was happier and secure in knowing his home was still out there.
But just as the Moment took its own spin on the whole Rose/Bad Wolf entity, it probably decided to alter the fourth Doctor and age him a bit. Just the right person the Doctor needed to see to motivate him in his search for Gallifrey.