Bob, There is a gyroscopic event that happens around this speed. I don't remember the correct name, but it is during the transition range from steering normally to using countersteer. The design of the bike, very roughly say a race frame vs. a touring frame, headset tightness, tires and possibly anything else will determine the severity of the unstability and at what speed it happens.
Brad
PS With motorcycles a second transition happens at a much higher speed, over 100 MPH.