You'll need a separate Bluetooth transmitter that can use the DFPlayer's analog output as it's input. (I don't happen to know of one but I'm sure they exist.)
The DFR player does all of the "work" and is simply controlled by the Arduino. The Arduino never sees the digital audio data (or the analog signal).
The analog & Bluetooth can work simultaneously, fed from the DFPlayer so there shouldn't be any extra software. (The Bluetooth board should also work stand-alone and run from its own built-in firmware.)
I think that the DFR player wouldn't need an Arduino, because it can be controlled just by the ADKey Board.
Then maybe the Arduino could be needed for the Bluetooth transmission. How do I find a "can use the DFPlayer's analog output as it's input"? How can one look this up?
I am sorry, if I knew how to find it, I'd do it myself