draw the fbd of the bide when its inclined and not inclined.
forces will be:
1. mg, vertically down. from COM/COG
2. normal, vert. up. from pt. of contact.
3. frictional force, horizontally left.
if the bikes not inclined, there will be an unbalanced clockwise torque and the bike will topple.
so the biker bends thee bike in the direction of the turn.
a car on the other hand, has 4 wheels, and its mass is substantially more than that of the bike.
the car will have a linear velocity before it enters the turn. so it will have a tendency to go straight. it is because of this tendency that the car bands towards the right.
the frictional force will still be there, but because mass is so much angular accln. will be very less. and also i think, the torques will get cancelled.
EVER HEARD OF BODY ROLL IN A CAR?
its because of this and the suspension setup of the car.