TexasCHLforum.com

So I know I've read in the penal code(don't remember exactly where I read it) you can carry your weapon concealed or OC legally without an LTC if you go from one location to another and are allowed to have your weapon at both locations. So you can carry your firearm at your house, you can carry at the range, travelling directly from one location to another is covered.

Now Public transportation may be a whole other ballgame/issue - not sure what Metro's policies on unlicenced carry are, but as long as you don't detour from home, to bus, to range - then I believe it would be perfectly legal. Maybe consider using something like Uber instead ?