Ok fellas what you are hearing is your speaker/audio wires picking up the inductance given off by a wire carrying power. There are a couple of ways to rid yourself of this and you may need to get creative. For the easiest way which you're out of luck with would be to ground one end of the shield in the speaker wire which won't happen because you aren't using shielded wire. Now you have a couple of more options, try to locate/move your speaker wires as far away as possible from any wires carrying power (ie: blinkers, tail light, fuel pump, spark plugs, etc etc). A bike being so compact it may be difficult to locate the wires where they won't pick up any inductance given off by a power wire but you may get lucky?
Biker you may be able to wrap you turn signal module in aluminum foil (yea its a redneck shade tree mechanic fix) but it should work. The aluminum foil will act as a shield, you ever tried to use a cell phone in a trailer that's made out of metal, doesn't work too good huh? It's the same principle except your keeping the inductance inside the foil.
Another trick might be to try and put a few twists in the speaker wire at the speaker. These twists may impede the inductance from getting to the speaker, that's why computer cables are twisted to help remove and prevent interference. Let me know if any of these work.