Whatever bike you have now will probably work just fine for a sprint tri. After you've done a couple, you'll have a much better idea of your "perfect" bike.
I did my first sprint on a hybrid upright commuter bike with rack, fenders, and sprung saddle. (passed a sh*tload of people, too) There were women kickin' @$$ on mountain bikes.
For your first couple tris, the strength of the rider is far more important than type of the bike. Save your money for now, your experience will guide you better than any of us ever could!
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson