I filed a report at http://www.apple.com/feedback/iphone.html .
I hope more comes out of it than my trip to the genius bar did.
Here's the report I filed:
Since iOS 7.0.3 was released, I have been experiencing high data usage, both cellular and wi-fi, whenever I use the Music or Podcasts apps on my iPhone 5. I am now running iOS 7.0.4 and the problem is still present.
I've detailed the problem in this thread on the discussion board:
https://discussions.apple.com/thread/5591663?answerId=23943379022#23943379022
I have limited bandwidth for wi-fi due to a 25 GB/month cap on my internet via satellite service. Before we isolated the problem to theses two apps I was using over a GB a day just on my iPhone and with other internet activities we would have used our monthly bandwidth in just a few days.
The Genius and I restored my phone to factory conditions, and even after that the problem still occurred. She advised me to report the problem here.
Thanks to all those who commented for your ideas.