Even if former President Obama disagreed in most topics with his predecessor: former Presdient Bush, he can show respect to his predecessor by acting "presidential:
Keeping those policies that were enacted by Bush, and that he agrees with, as long as they are working for the benefit of the country. Doing this instead of backtracking every policy simply because his predecessor issued them is acting presidential.
Employing fair criticism toward his predecessor, without employing fallacies, or excessively partisan arguments.
Working with those who were part of the former administration if it is for the benefit of the country.
