You can unlock a bonus car and different paint schemes for it by simply having a Team Rush account with enough mileage accumulated on it.

Unlockable	How to unlock
Black paint job (for secret car)	Mileage = 1000
Black/fire/white paint job (for secret car)	Mileage = 1500
Blue paint job (for secret car)	Mileage = 200
Cop Car Paint	Mileage = 10000
Orange paint job (for secret car)	Mileage = 5000
Red paint job (for secret car)	Mileage = 2049
Secret car with yellow paint job	Mileage = 100
Yellow-green paint job (for secret car)	Mileage = 400