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Some pieces of jewelry may show better on black, but eliminating all of the dust is rather challenging. I would avoid placing jewelry on a mirror because you can get double reflections. Some folks use light tents, and others don't. If you decide to try a light tent, it's pretty easy to fabricate one with white rip-stop fabric and PVC pipe. Any modifier, including rip-stop, can cause a color cast, so use a grey card or Color Checker Passport (or similar) to nail the colors.
If you already have diffusion panels, the white ones can be used. Your pair of SB-700's will be adequate, and you'll obviously need a way to trigger them off-camera. As already suggested, manual mode for the camera and lights is the only way to go.
Here's a sample shot with a 105VR Macro that demonstrates the difference between black & white backgrounds.