<< If you plead not guilty you tell your side of the story right there, then the cop tells his side, then the judge says guilty, then he nails you with big fines :| >>
Not here. In California, you show up for an initial hearing. No witnesses are expected to come. If you plead guilty, they deal with your fine right there. If you plead NOT guilty, they schedule a second date, on which you should bring evidence and witnesses. They also call the cop and tell him to come in on that day.