If both you and the person on the dirt bike were determined to be at fault in the accident than it would appear each party would take care of their own damages. If that is the case then unfortunately having only liability insurance on your motor vehicle would not cover damages your auto sustained in the wreck.

BI and PD liability insurance typically covers bodily injury that you cause to another person or property damage that you caused to another vehicle or person's property. Liability insurance does not cover your own vehicle for damages resulting from an accident.

For your vehicle to be covered for damage it received in a car accident, you would need to have physical damage on your vehicle in the means of a collision coverage. A collision coverage policy would cover damage to your car when your car hits, or is hit by, another vehicle, or other object.