Set up quandry

[RS]

Problem resolved, please delete post.

[J.D.B.]

Where's the buzz/rattle coming from? Out on the frets? If so, add a little more relief and see if you "move the needle" any. I take it the DR's are new to this instrument? Sounds like they may have less tension than the previous strings, and so vibrate wider.
Josh

[Just Thumpin']

Don't mess with your setup until you replace the string first. I have had several bad strings over the years that have done exactly the same thing. If you cannot visibly see anything rattling, try a new string...

[chowlee]

If you have elephant ears tuners, check if one of the ears is loose. Many are.

[XylemBassGuitar]

So, you've got a little relief, you're sticking with the same string gauge, the nut's not too wide....hmmm....

Try to replace the string (like Just Thumpin' says) and tighten all of your screws and such.

If that doesn't work, loosen the truss rod to give the neck a little more relief, sometimes buzzes on the frets near the headstock can be adjusted out with the truss rod...

If those ideas don't work, definitely let us know how you end up fixing the bass!