You can't use the GI Bill to pay for a private pilot's license by itself. There are 4-year college programs that offer a private pilot's license to you for "free" by consuming your entire GI Bill in exchange for 12 months of flight training spread out over four years.
You can however use the GI Bill to pay for flight training after your Private Pilot's license provide that you do it with a VA approved part 141 flight school like Flex Air. There are additionally some ways to co-enroll to reduce your costs.
Read our detailed guide to the GI Bill and VA Benefits for flight training.
Also see our guide to VR&E for flight training.
GI Bill® is a registered trademark of the U.S. Department of Veterans Affairs (VA). More information about education benefits offered by VA is available at the official U.S. government Web site at www.benefits.va.gov/gibill