External mic with iPhone and Bluetooth output
I found this app on App store that might suits your needs.


  Megaphone transforms your iPhone into an instant Microphone, PA system
  or Megaphone when you plug it into amplified speakers.


https://itunes.apple.com/us/app/megaphone-free/id304955183?mt=8

As you plug in external microphone your system should switch to that input, same for the Bluetooth speakers as output.