Any vehicle will drift to the right on most roads. Roads are crowned for water run-off. Corners are banked to aid turning.
Body position affects turning or drift. Road racers shift to the inside of the corner and even hang their leg out. Dirt riders weight the outside peg to help maintain traction and direction in a corner. Street and dirt riders press the tank with their knees to aid direction changing. A passenger leaning away from a turn as you lean in will cause you to swing wide.
Even if you were able to find a table top level road, the bike would drift one way or another depending on your body position.