It’s not true Bush did not try to help protesters, but his efforts were counter-productive. And Obama is continuing the same policy, slightly modified:

usatoday.com

Bush expanded the program in 2006 to $66 million. Iran responded by arresting and cracking down on activist groups.

Obama decided to continue the program, but the funds were not specifically marked for Iran, but for “Near Eastern Regional Democracy Initiative”, which could just as easily be targeted for Israel as Iran.