Not certain of the circuitry of your music player.
Try the following:
Connect music via Bluetooth, (output low as it is).
Can you hear the music in both speakers or only one? If only one then which one left or right?
Next, leaving the Bluetooth music playing, plug a jack into the socket, it doesn't have to be connected to anything at the other end. If the music stops it proves that the socket disconnects the Bluetooth music to the amplifier.
Depending on whether you did hear the Bluetooth music in only one speaker and which one will influence what you may look for next.
With a lot of sockets there are changeover contacts connected to both the 'tip' and 'ring' connecting springs of the socket. This means that when a jack is inserted these contacts break the existing input circuit to the amplifier section (in your case the Bluetooth music) and connect the jack input to the amplifier circuit.
The convention is that the left speaker is connected to the 'tip' connection and the right speaker is connected to the 'ring' connection. The 'tip' is the end of the jack furthest away from the cord and the 'ring' is the next one after the insulating spacer. The last connection is known as the 'sleeve' which is closest to the cable and is used for the 'common' for both left and right speakers.
So if you are not hearing music in the left speaker and your socket does have the changeover contact configuration you need to check the connections to both these contacts associated with the tip connector. The same goes for if you have no music in the right speaker you need to check the ring changeover contacts connections.
If the music is in both speakers and connecting the jack does not stop the music you may have the other type of socket where there is only a single contact used which either makes or breaks when the jack is inserted and this is used to "tell" the amplifier to switch the input source from the Bluetooth to the socket. It may be that you will have to trace back the circuit from the amplifier input, (following where the tip and ring connections from the socket go will probably lead you to the input) then see if there are other paths that hopefully will lead you to the Bluetooth output and that you may spot the problem. Perhaps a broken connection or a dry joint.
Sorry I cannot be more exact and that hopefully it is of some help.