Bullock filed for divorce on April 23 in Austin, Texas, where she maintains a home and discreetly used her backwards initials "B.A.S." and James's initials "J.J.G" on the paperwork.
"Her legal filing indicates that both she and Jesse are seeking an amicable settlement and that there will be no children at issue in this divorce," says Daryl Weinman, an Austin-based family law attorney who's not involved with the case. "I wouldn't be surprised if this divorce wraps up quietly within two months."
The lawyer adds that Bullock has no legal rights over James's three children and if she wants visitation, she'll have to request that from a judge in a separate proceeding. The former couple could also reach a private visitation agreement. Bullock has said she intends to remain in their lives.
Although it's unclear from the papers whether they have a prenuptial agreement, James won't be entitled to spousal support, Weinman explains, because in Texas a couple must be married for a minimum of 10 years for a spouse to qualify for support.
As for Bullock's use of initials instead of her full name on her filing, Weinman says, "I've never seen anything like that before. It's clear that Sandra is seeking as private a divorce as possible."
Meet Sandra Bullock's baby! For the whole story – including photos of her son Louis, an emotional interview about her breakup with Jesse James and her life as a new mom – pick up the new issue of PEOPLE, on newsstands Friday