I ran into this at the Santa Monica Pier shooting in the amusement park. The security guard very politely and professionally asked if I was shooting commercially. I stated no that my images were for private use. He said if that was the case to please follow him to the administration building and sign a statement affirming that my shots would not be used commercially and then I could shoot to my heart's content. While it was confrontational, it was not hostile. The security was/is very well trained at the pier.
This is a policy of the City of Santa Monica, not a federal regulation. I'd call the people who manage the mall and ask for permission to shoot from the bridge ... I seriously doubt if they have a policy similar to Santa Monica.
Gary