Bumped a car from behind at a stop light?

I was in the line at the stop light today and the light turn green i looked at the front of the line and the cars began to move and the car in front of me turned off their brake lights i left off my clutch and put my car into first gear, then the car in front of me apparently let off their gas to change the song on her ipod and their car slowed down faster than i could and i bumped the back of their car it left a few tiny hair line scratches (no damage to my car) that were barely visable to the naked eye. I told her that i could give her my name number and address and pay to get the scratches removed she refused saying her father said she should call the police following that university police department came gave me a $149 careless driving ticket and she refused to let me pay cash for her damages and is contacting my insurance agency. I am 19 years old have one previous speeding ticket. What are my options, i do not want my insurance rates to rise for such a minor incident and is their any way i can repeal the ticket since she was not paying attention to the green light? i just feel like I am getting charged a lot (ticket,driving school,insurance deductible,rate increase) for an accident that damages could be fixed for under $100 dollars