I just visited the Bexar County Sheriff's Office site,which of course is who runs the Bexar County Jail. Since I used to live in San Antonio, the first answer to this question was interesting. I didn't realize that there was an inmate list that you could get online. But, apparently, at least at the Bexar County Jail, there is no inmate list on the internet site, at least that I was able to find. If you find one, I'd sure like to know.
You can just go in the internet and type in Bexar county jail and then click on inmate list. Or you can call the jail and ask.