I suffer the same problem. My Schwinn Shimmies pretty bad around 18-20. havent really taken it faster than that. Assuming its the dish on my front wheels.

My Centurion has the same problem up around 20, but its not as pronounced as the Schwinn. Did it with the stock wheelset, the wheelset that is now on my schwinn, and my 105/cxp22's. I think it might be me.