“No Parking” Ticket in Washington D.C.

I’ve got my first parking ticket today and would appreciate any helpful information. I came to pick my wife and baby after a doctor appointment on K st, NW at noon. No parking spots were available and I’ve stopped in front of the building in bus stop zone (but not blocking the stop itself) with engine turn on and emergency light turn on. I didn’t leave the car, sit inside all the time. After little more than 1 minute waiting the parking enforcement woman appeared in front of my car and start issue me a ticket. I opened the window and ask what does she doing, but she just gave me $100 !!! ticket and said I waited too long. Later on a day I’ve spoke with another parking enforcement guy on a street and he said in this situation they always ask first drivers to move and only if they still standing issue a ticket.

So two questions:
1. Do I have chance to beat this ticket? I have a proof from the doctor’s office of the appointment time.
2. What will happened if just to ignore this ticket? I’ve drove rental car.