Run helps biking more than biking helps running I have found. That said, only running 3 miles at a time isn't going to help much. I have found that running very steep hills is good training for cycling since it uses mainly your quadracepts and to a small degree replicates cycling motions, but that is only on very steep terrain. If you can find some moderate hills, you may want to look into doing some long interval repeats, at the very least it will help your body increase its ability to deal with lactic acid buildup, I'm guessing a single speed race would produce alot of lactic acid.