my one and only iPod is long gone. I regret that I actually bought the docking cradle made by Wadia. It extracted the files on the hard drive and bypassed the Apple DAC . It was truly a great product, worked as advertised, but hey they still were mp3 files, and who wanted to haul the iPod out of gym bag anyway? I probably used it 3 times and then donated it to a thrift shop.
Anyway, if anyone actually knows if the iPod did Bluetooth, please chime in. And if it did do bt, it was probably the first BT codec, which sounds awful.
OP, use your phone as a source into a BT receiver, you will be much happier