Not sure what the point of the implicit operator overloads was. Why not just have:

  public class CreateBooking {
    public int TypeId { get; private set; }
    ...
    public CreateBooking(BookingTypeId typeId, ..., ...) {
        TypeId = typeId.Value;
        ...
    }
  }

  public struct BookingTypeId {
    private readonly int _value;

    private BookingTypeId (int value) {
        //...some simple validation logic...
        _value = value;
    }

    public int Value { get { return _value; } }

    public static BookingTypeId Custom(int value) {
        return new BookingTypeId(value);
    }

    public static BookingTypeId Gold() {
        return new BookingTypeId(3);
    }

    public static BookingTypeId Silver() {
        return new BookingTypeId(2);
    }

    public static BookingTypeId Bronze() {
        return new BookingTypeId(1);
    }
  }

With the added bonus that you're using less fancy stuff, so you don't need to explain to the junior dev that gets to maintain it what's going on.