The three males were identified as Devin Banks, 19, Pascal Okadigwe, 19, and Cristian Lloyd, 21.
Authorities say a 52-year-old woman waiting for a bus was hit by one of the rounds fired off by the suspects who were being chased by deputies.
The Harris County Precinct 4 Constable's Office said the shots were fired in the 1300 block of Gears Road, between Greens Parkway and Ella Boulevard, around 4:30 p.m. Friday.
According to the constable's office, patrol deputies saw a Toyota Camry with three people in the area. The deputies say shots were fired in their direction by the suspects in the car.
None of the deputies were hurt, but an innocent bystander at a nearby bus stop was shot, according to the constable's office.
Constable deputies tended to the woman and applied a tourniquet to the victim's wound. She was taken to the hospital, where she is expected to recover.
After the shooting, other deputies chased after the suspects, taking Okadigwe and Lloyd in custody. Authorities searched for Banks near an apartment complex not too far from the shooting, but were not able to find him.
Banks is being charged with aggravated assault with a deadly weapon and tampering with evidence. A warrant has been issued for his arrest.
Deputies later found out that a round from the suspects also struck an Aldine ISD school bus. The driver who was the only person on board was not injured.
Investigators also learned that Lloyd attacked a 60-year-old woman and stole her car keys in an attempt to steal her vehicle before being arrested.
Lloyd and Okadigwe are both being charged with aggravated assault with a deadly weapon, robbery, and felony evading in a motor vehicle. They are being held in the Harris County Jail.