I think that is a shoulder not a bike lane. It may be illegal to drive/make turns in a shoulder, but it arguably is safer (regarding rear-end collisions) and more efficient for cars to move over when making this turn.

It is completely legal to drive on an improved shoulder in Texas, the only difference (that I am aware of) is that you cannot overtake (aka- "pass") another vehicle while traveling in the shoulder.
I do hope the school zone wasn't active while you were taking photos and driving though.

Just remember to drive friendly, the Texas way.

To ANON turn signals use and motorists slowing would also help the situation of turning off the larger arteries of this fair city

Resolved.