Actually it doesn't go quite straight forward like that. In most Android standard Bluetooth implementation, the music you are playing will be sampled to 48kH PCM first (via Android internal SRC, which is default to 48kHz unless the manufacture uses a more advanced SRC), send to the Bluetooth chip to be resampled using the Bluetooth codec (*this is where your setting 44.1kHz vs 96kHz will take effect), send over wirelessly to the headphone's (or BT DAC/amp's) BT chip, resampled back to PCM (*bitrate + bitdepth depends on the DAC chip inside the headphone as well as how the manufacturer configuration though oversampling is the usual choice) and then decode to analog sound.
So even if you use 44.1kHz for your Bluetooth codec setting, the music would very likely have been resampled before and after the Bluetooth transmission and your setting won't affect those at all.