Have you had Bluetooth on before this or did you turn it on to work with the Garmin?
I'm using Android so I don't know how relevant my experience is to you, but my battery doesn't drain like that. It's mostly the screen that drains mine, or being out of range (of a cell tower).
Have you tried stopping the Connect app? I'm guessing it won't be able to forward texts that way, but I've never used iOS.
You should be able to ride for several hours, take as many pictures as you want, use the maps on the phone, etc. You can carry a battery pack for your phone and even charge it in a jersey pocket while you ride, but you shouldn't have to.