Quick checks:
Take the offending string off and reinstall it.
Try a piece of paper under the nut (although I have played plenty of fretless basses that have the nut flush to the fingerboard and are fine)
Raise the saddle height to see if you can get it to play clean. It may only need a very small lift to clean it up.
Check the fingerboard is smooth under the string (i.e. no string marks, nicks, slight bumps etc.)
How straight is the neck? I find a very small amount of relief (say .25mm at the 9th fret when you press down at the first and last "fret") is enough to let the strings breathe.
Good luck!