If you have a decent auto parts store near you, they should be able to help. I have almost the same light, and I believe it's a 6 volt bulb. You'll just have to match the watts, and the type of base (I'll check mine tomorrow and get back to you).
Also, you might check to make sure you have a good ground at the base of the bulb. I ahd this problem with a headlight made by Union, so I'm not sure how the Schwinn light is grounded.