Freddy Ford, a spokesman for George W. Bush, who has a home in Dallas, declined to comment.
Free email accounts from commercial providers are especially vulnerable to hackers who exploit easy-to-use features to reset email passwords. Many passwords can be reset by a hacker who discovers, for example, the birth year of a person's mother, a father's middle name or the name of a favorite pet.
That's what happened to former Alaska Gov. Sarah Palin in 2008, when she was the Republican vice presidential candidate.
"That's the first thing I thought of," said Tyler Moore, an assistant professor of computer science at Southern Methodist University in Dallas. "The key here is when you're famous or a well-known person or celebrity, there's not a lot you can do if you're targeted."
A Tennessee college student named David Kernell was convicted two years later on federal charges.
Last year, Republican presidential candidate Mitt Romney's free Microsoft Hotmail account was hacked after The Associated Press revealed that he and some top aides had used private email accounts to conduct state business at times when Romney was governor of Massachusetts.
The anonymous hacker claimed to have guessed the answer to a security question about Romney's favorite pet to gain access to the account and change the password.
Email security is "a constant concern" in presidential politics, Romney senior adviser Eric Fehrnstrom said Friday.
"What we learned is that no matter how secure you make your system, there is someone out there spending every waking minute trying to subvert it," he said.
Last year, a group of hackers known as the D33D Company published a list of what it said were usernames and passwords for more than 450,000 email accounts, including more than 25,000 AOL accounts. It was not immediately clear whether the Bush family's hacked AOL accounts were among those.