Do I need a permit for garage conversion in Bexar County (Unincorporated)?

Most likely yes. Garage conversion usually requires a permit in Texas. Confirm the specifics with Bexar County (Unincorporated).

Section R105.1 of the 2012 International Residential Code that Texas cities enforce requires a permit to alter a building or change its occupancy, which covers turning a garage into living space. Texas adopts the energy efficiency chapter of the International Residential Code as it existed on May 1, 2015 as the statewide energy code for single-family construction, and cities must administer and enforce it (Health and Safety Code 388.003), so the new living space must meet those insulation rules. Every sleeping room needs an emergency escape opening (Section R310.1). Permitted alterations require smoke alarms as in a new home (R314.3.1) and carbon monoxide alarms where the home has an attached garage or fuel-fired appliances (R315.3). Turning a garage into a bedroom, living room, office or apartment changes it to habitable space, which must meet the code for living areas, such as insulation, heating, ceiling height, light, and an emergency escape opening in any sleeping room. A conversion normally needs a building permit, and often electrical, mechanical and plumbing permits too. Zoning may also require you to keep off-street parking or limit a second unit, so check zoning before you design.