It sounds like you may have too much relief (neck bow/upbow) with your saddles too low at the same time. If this is the case all will be well until you get up into the higher frets and then the strings will start getting choked off by the highest frets. If your neck is too flat you will get buzz lower down (first few positions) and if you have too much curve the buzz will be higher up like in your case.
Put a capo (the clamp thing that guitarists use) on the first fret and then fret the last fret (20th to 24th depending on the bass). There should only be about 1mm of space between the 9th fret and the strings. By the sounds of it you probably have more than this. Loosen the strings and give the truss rod a quarter turn clockwise. Tune the strings and let it settle. Repeat this process until you have that approximate 1mm. You can now adjust bridge saddles to taste.
Read this:
http://www.tunemybass.com/bass_setup/