i'd been looking to do something like this and fount this tutorial, it shows how to follow a specific path. It works with a car (a CALayer) and a UIBezierpath as the race track and is solved in this order:
Defining the path the car should follow (in this case your BezierPath)
Drawing the black line that defines the track; (N/A)
Drawing the white dashed center-line of the track; (N/A)
Creating the layer defining the car; (your Layer)
Animating the car along the path. (What your asked!)
You can check the reference Post here:
http://nachbaur.com/2011/01/07/core-animation-part-4/
Also you can download the source code here:
http://cdn5.nachbaur.com/wp-content/uploads/2011/01/CALayerAnimTest.zip?25881d
hope this helps!
regards,
Jorge.