Using Enum to represent VehicleType in cab Booking system

I am working on low level design of cab booking type of system and feeling stuck at modelling Vehicle in Booking class.I came up with following design.

Class Vehicle
{
    
    
}
Class Car extends Vehicle
{
    
}
Classs Bike extends Vehicle
{
    
}
Class Auto extends Vehicle
{
    
}
Class Booking
{
    int number;
    ...
    ....
    Vehicle Vehicle;
    VehicleType type;
    ...
    ...
}
enum VehicleType
{
    CAR,
    BIKE,
    AUTO
    
}

Now to see, which vehicle is used for booking, we can see the VehicleType from booking and then typecast the vehicle to that object(CAR,BIKE,AUTO).Is it a bad way model?

In general, if we have a reference to parent, and we want to know specific child class which is holds,is this a good way to do?Are there alternate approaches ?