The bluetooth adapter isn't making the hard drive noisier - it's picking up noise the hard drive makes that's already there that's so faint it's not normally noticable and amplifying it.The bluetooth adapter is picking up the radio frequency noises made by the hard drive. The noise you hear will decrease with the square of the distance from the hard drive, so the farther away from the hard drive it is, the less noise you will hear.
E.g. if it's twice as far away from the hd as before, the noise volume will be 1/4 of what it was.
I've had the occaisional sound card that does that - I moved the card as far away from the hard drive as I could.
Make sure that the sides of the cases are installed - they will block most of the noise. If there are any open drive bays or slot spaces, install something in them, preferably metal.
The case should ALWAYS be grounded through your AC power connection, all the way to the AC source - if it isn't, it's a lot more likely you will pick up unwanted noise when you connect certain things to the computer.
Try plugging in the bluetooth adapter into a port on the case front, or into a male/female USB extension cable.
OR try NOT plugging in the bluetooth adapter into a port on the case front - the wiring to many USB case ports is not properly shielded and you will pick up more radio frequency noises if you plug into those ports.
The same goes for cheap external USB hubs - two or more ports connected to one USB port directly connected to the mboard.
You will probably get the least noise if you connect it to a well shielded male/female USB extension cable plugged ito a port directly connected to the edge of the mboard at the back of the case.