That's odd. Let me think as I type...
Possibilities I can think of are:
1. The 7th fret is just a little high
2. The 6th fret is too low
3. There's something loose somewhere that vibrates harmoniously with the D# played on the A string, either on the bass or in the room if you're playing amplified (try quiet or a different room as a test of the latter)
4. The string is bad
I don't see any way that setup should give you a buzz on just that one fret and that one string. Also, the fret being low/high seems unlikely as it would probably be evenly low/high causing a buzz on multiple strings at that location.
If you tune up a half step, does it still buzz? How about down? Does everything that gets screwed down seem to be screwed down (tuning pegs, etc)? You could also try holding a straight edge the length of the fretboard to see what sort of bow you have in the neck, and that it is even across the fretboard. Pressing down a string at spots on either side of the problem area can simulate this fairly well.
Also, you could try cutting a tiny/thin piece of cardboard or folded paper and loosen the string enough to place it under the bridge saddle to temporarily raise the string at the bridge. Tune back up and see if the buzz is still there. If it goes away, then maybe raising the bridge a tiny amount will clean it up for you. Work in tiny increments.
Make sure before you go messing around with setup, cause if you're not comfy with what you're doing, it may take a while to get it back where you like it.
Also, I am assuming that when you say 'new', you mean fresh-from-factory and not just new to you, so I am discounting worn frets as a possibility.
Just some ideas to maybe get you closer to the problem source. It could just be a bad string that needs to be replaced. One last thing to consider is whether this ever worked to your satisfaction, or was it always a problem. If the buzz wasn't there before, what may have changed?
