Unless you meet one of the state's exceptions, YOU MUST PURCHASE A FISHING LICENSE.
With your license, you can fish in almost any public bodies of water within the state of Texas. You can either purchase the license online, buy it from an official License Agent/Agency, or call the San Antonio TPWD office at (210) 348-7375.
Fishing along the San Antonio River Walk published by the San Antonio River Authority on Feb 1, 2021
Unfortunately, there are no public areas in Bexar County where you can fish without a license. In Texas, the only public places that allow fishing without a license are state parks. The closest state parks with fishing available are:
Guadalupe River State Park in Spring Branch, TX
Lockhart State Park in Lockhart, TX
Palmetto State Park in Gonzales, TX
Blanco State Park in Blanco, TX
Garner State Park in Concan, TX.