Better way of using the iPhone with a Bluetooth speaker
I figured out my own answer, so hopefully this helps whomever runs into this problem.  

Bring up Siri by holding down the Home button.  It will come up and on the bottom left you'll see Audio source indicator, pictured below (and highlighted in yellow).



As you can see, it has a grey background.  Tap on it and you'll get a menu of audio sources (typically your phone and the Bluetooth device).  Select your phone.  The icon will get a white background indicate that you successfully changed the audio source.  

Now switch back to your Text Messaging application and the tap the microphone button on the keyboard and it will now use the phone microphone instead of the one on the Bluetooth device.