Bundick was charged with murder and aggravated assault with a deadly weapon in the July 3 killing of 20-year-old Rashad L. Minix of Houston and wounding of 19-year-old Ferunell Smith.
Police say Minix suffered multiple gunshot wounds. He was pronounced dead at Ben Taub Hospital. Smith was taken to the same hospital. Doctors say he is expected to survive his injuries.
Bundick is in the Harris County Jail. His bond is set at $100,000. An attorney for him was not yet listed in electronic county records.
The Associated Press contributed to this report.