Price told The Associated Press on Friday he believes the two were under the influence of narcotics and "thought they needed to get a ride home."
The Galveston County Daily News reports a police dispatcher monitoring security video Wednesday night noticed the pair.
Price said the woman, who received medical attention, recovered and will be cited for public intoxication. Her name was not released.
Michael Carl Bell of Texas City was jailed on a marijuana possession charge. A Galveston County jailer, who declined to allow her name to be used, said bond was $2,592.
Price and the jailer had no information on an attorney for Bell.