Unfortunately it's currently not possible to use your phone as a simple playing device using wifi or Bluetooth.
Here are a two things you can try:
Stream files from your PC to your phone:
This can be done for example using one of the DLNA / UPNP players (e.g. Smart Player) in the store. Or even complete streaming solutions like Plex.
Or use one of the ...
This feature is now available (as of March 2015). Any music files in supported formats (MP3, M4A and WMA) you add to your OneDrive Music folder can be streamed through Xbox Music on your phone, PC, Xbox or the web player.
For more information see Blogging Windows and Windows Central.
BBC is probably using HLS, a standard that requires an app by the provider.
The Swedish public TV, SVT, uses HLS as well. They have an app you can download that will enable HLS for svtplay.se.
Send an e-mail to BBC and ask them to do the same.
The only way to get iPlayer working on Windows Phone 7.x is to convince BBC to write a version of iPlayer that works on that particular OS.
The only people who could tell you if it's a technical limitation is BBC itself.
There are no work-arounds. It's likely a lack of resources at BBC that have thus far prevented them from porting iPlayer to WP7. And ...