A dropping stem?
What I meant Mike, is that there are quite a few things you can try before spending hard earned cash. Once you know more and know you enjoy TTing, then buy. buy, buy!
Getting yourself low and aero is what matters. Then helping the flow around you with nice deep wheels and a helmet will add to that. As for gears...
try your fixed with a low end, you may be surprised!
Edit: As others have said before, you don't need a bling bike. Just one that would permit you to get aero. A lot of the guys at the club have TT or track frames, with nice bars and wheels, but their gears are not necessarily as nice as on their Sunday best.