Straffo-
A "good Christian" realizes he is no better than anyone else WRT committing sin, but does reflect on his actions, recognizes the fault, and asks God for forgiveness. The sinner then must turn away from those actions.
What you are alluding to is the concept of a person going out and committing whatever acts he wishes, then getting the cure-all forgiveness, only to go out the very next day and do the same thing again. You're right, that is not true repentance.
In the case of Bush, assuming the story is true, the repentance is real IF Bush felt the guilt, asked God's forgiveness, then turned away from committing the same act again. So... unless someone can drudge up the string of abortions arranged after that fact, the repentance would appear to be real.