There are bikes and cars in D20 Modern.
There are several D20 Modern links on the new vault, some with additional material, but I think that's the main one.
The vehicles don't work like horses (you'd need a whole new animation set for that). They're creatures. I imagine that when a player uses a placeable car, they turn into a car appearance (or something like that).
NWN_baba yaga is right, cars turning on a pivot do look odd. The effect is most ludicrous with very long vehicles, such as the coach-and-horses in CEP. Maybe you can live with it for shorter cars. Alternatively, you can script them to follow a curved pattern of waypoints, as in the following example by Shadooow:
That video has additional features - the cart is a tail, so the player can sit in it - speed is varied on bends (which I imagine to be a lot of work) - but you could do something simpler for cars (if D20 Modern doesn't do it out-of-the-box).