Hi Bruce.
I have reconnoitered that before for the possibilities, and ruled it out. I've also never heard of anyone paddling it.
There are three "Bernard" creek crossings of FM-1093, from east to west they are called: the East Bernard, San Bernard, and Middle Bernard. Oddly, the Middle Bernard is the west-most branch.
The East Bernard and Middle Bernard normally don't have enough water at FM-1093. And all three are very narrow. Of the three, the middle one, the San Bernard, has the best potential.
The San Bernard may just be barely passable at higher water levels, but normally it's low water, exposed sand bars, and downed trees. I've always had this on my to-do list, but every time I drive that road and stop to look at it, it's never suitable.
I'm also not sure it is a public waterway - it may be private property.
I think the TPWD is wrong on this one. At least from the FM-1093 access point. Unless maybe you go right after a lot of rain when the prairie is draining and raising the water level in the creek.
Photos from FM-1093.
East Bernard, looking north:
East Bernard, looking south:
San Bernard looking north:
San Bernard looking south: