I have actually had string buzz on one string/fret before that was the result of very old strings. Changing to new strings solved this problem.
Fret buzz on the first few frets can also be the result of an overstraightened neck so introducing some relief into the neck (loosening the truss rods) is the solution in this case.
You may also have a high fret that needs to be dressed a little.
However I would just try changing strings first. If the strings are very old anyway why not get a fresh set of your favorite strings and give your bass some TLC

Maybe thats all it needs.