Will I be able to plea bargain my second traffic ticket in a one-month period?

Last month (end of February), I received a "Failure to Obey a Traffic Control Device" ticket in the TOWN of Tonwanda for getting on a thruway entrance that was closed. However, because it was not apparent that the entrance was closed (no sign or proper blockade), they let me plea bargain it to a parking ticket and traffic school. Just took the traffic school and need to pay the parking ticket fine. Now, last night, in the CITY of Tonawanda, I got a speeding ticket - the cop said I was going 42 in a 30, but my speedometer never broke 35. He explained that if I show up to court I can plea bargain it down and get no points - but, you can only take traffic school once every 18 months I believe. Will I still be able to plea bargain? Never gotten tickets before this month - having awful luck.