A good number of new racers use the one bike for everything. Here is a way to do it(tire is the big sticking point, you just have to use a good general purpose tire).
One set of bars, brake, and stem for the road. Another stem and bars for the track. 48 up front; 17 for the road/ warming up. 15 on the other side for the track.
That should get you through at least the first half of a season, if not the entire.