I used to take my oldest (9yo now) on the bike until we almost became the hood ornament of a redneck racing diesel (lifted Dodge 4X4) on private property. Shortly after, my boss' 19yo son (also a friend of mine) died in a motorcycle wreck.
I don't think I'll let her on unless the circumstances are ideal....but even then??? She loves riding on motorcycles though. Even after a good, 10 yard, gravelly low side.