Not sure about Bexar County. Wilson County requires at least 10 acres if your property is in a platted subdivision. I could find no minimum acreage requirement for property outside of a platted subdivision.
State law prohibits counties from enacting certain rules on property over 10 acres. I'm paraphrasing severely here, but that's probably why you've heard that. And just shooting occasionally is quite a bit different than establishing a permanent range. You should just check your county's rules.
In another county where I want to find the answer to this question, the people at the County commissioners court were very helpful over the telephone. I would search for that information online and give them a call.