Sounds like the SSD case is not shielded or does not have enough shielding. Protecting the rest of the logic from it's EMI/RFI noise (in your case the WiFi & Bluetooth antennas are picking up the noise).
You could try added some shielding around the SSD but be very careful not to have anything shorting to the added shielding.
To add shielding go to Home Dept or Lowes heating systems isle look for foil tape used to seal ducks (not duck tape!). Cover the drive with one strip and covers three sides (in a U) starting at the I/O connector and then back. Take a second strip and do the same across the rail sides. This time remove a patch of adhesive where the two strips cross over each other so you can make good contact between the sheets. Using packing tape secure this contact point and insulate any areas that could get to close to anything. The ground connection to the chassis is made by the mounting screws thru the foil.
The only rub here is the heat build up inside the SSD. Monitor it to make sure you don't over heat (try using one sheet across the rails if it gets too hot). The foil directly is not the problem it's the adhesive acts as a bit of an insulator.
Getting a metal/metal plated plastic boxed SSD should do better. Also make sure you have the power cord plugged into a grounded outlet as well (grounding doesn't help if it's not connected).