| Michael Campbel,
Without seeing the bass in person I can't tell you exactly what is going on, as there is a whole range of possible problems that could cause that fret to buzz. But, I can suggest some possible fixes.
1) Sometimes, buzzes near the nut can be caused by a neck that is too flat. Thus, loosening the truss rod a little bit may help to get rid of the buzz. A looser truss rod means that the strings can put a little more tension on the neck, giving it the right amount of upbow (relief). If you give the neck some relief, it may effectively "lower" the second fret in relation to the first, eliminating the buzz.
Warning: If you don't have any experience adjusting truss rods or are not confident in your ability to do so, talk to a professional luthier/repair tech in person before making any adjustments. Truss rods are relatively easy to damage, and are difficult and expensive to fix.
If you do know how to properly adjust the truss rod, I would try this first.
2) The fret beyond the first may just be a little too high. If this is the case, you'd need to take it to someone to level out/dress the frets.
3) If you are unfamiliar with stringed instrument adjustments, take the bass to a shop to get a setup. They should be able to at least tell you what is causing the problem, if not fix it completely.
Let me know how it goes. Good Luck! | 
