Well if the wire is also used as an antenna and the quality drops when the wire is not plugged, you're screwed.
There's no way you can transfer the antenna function over bluetooth.
The only way would be to have a tuner in your bluetooth headset and your player accepts this tuner as a kind of line-in.

To circumvent the problem, you have to check the following:
Does the bluetooth headset still work when the wire headset is plugged?

If yes there's a solution: buying or finding ultracheap wire buds. cutting the buds off, insulate each wire, use that wire as the antenna.
Most of the time, only a few centimeters are useful, so you can cut it to the need and glue/tape it behind the player, or wherever possible.

If not, you'll have to check if the player receives well without said wired headphones.
If it doesn't, you still have options, but difficulty increases... and I can't help you without knowing the device, and even then, if I can't touch it, I may not be of any more help.