Here's why reflectors are useless in the situation you described.
You were 100 yards (300 feet) from the intersection, when you spotted a bicycle crossing directly in front of you. Suppose you were traveling at 60 mph (90 ft/sec). It would have taken you 3.3 seconds to reach that intersection. In the meantime, the bicycle may have been traveling at 10 mph (15 ft/sec). The bicycle would have traveled 50 ft before you reached the intersection.
Let's further assume it would have taken you an additional 5 seconds to turn onto the street on which the bicycle was headed. The bicycle would have traveled an additional 75 feet. Thus, the bicycle would have been a 125 feet ahead of you at the time you actually turned onto the street.
Wheel reflectors would not be seen by you, once you and the bicycle were on the same road and going in the same direction. Something else would be required for the cyclist to be seen by you, e.g. taillights.
What did the wheel reflectors contribute? You saw the bicycle from a distance, in which the bicyclist was never in any danger. The bicyclist was long gone by the time you reached the impact point.