I think his real objective with regard to that bill was to get the border-security provisions stripped out, so he waged a general campaign against all illegal-alien-related provisions, on the pretext that these things were extraneous to the goals of the bill. I'm sure that even he knew he would look kind of silly arguing against increased funding for the BP while supporting the "REAL ID" provisions in the same bill.
I think that at heart Bush has no problem with any bill that increases federal control over traditionally state matters like drivers' licensing, especially when it provides opportunities for further surveillance and tracking of people.