This would call for some creative lawyering from a local guy who knows the judge and how the judge thinks. Because it is a traffic ticket and not a criminal charge, there is no rule that allows for removal, as the other guys said. The only thing that could be done is to file some kind of motion to reopen the case and ask the judge to then dismiss the ticket and order DHSMV to remove it from your driving record. DHSMV will do whatever a judge tells them to do. Getting a judge to do something hokey like that is another matter. Some judges might be sympathetic and play along to help you get your job (since you did the school and there were no points anyway) and others might look at your lawyer sideways and tell him to get the heck out of the courtroom with his crazy motion.
Wow. I had no idea these trucking companies were that tough! A three year old ticket with no points is the only thing you have and that is actually stopping you from getting a truck driving job?? I imagine if a company really likes you they might overlook it. But one thing is for sure, as the other guys said, you won't get very far writing the judge yourself.
I'm not aware of a way to actually remove an entry from a driving record, but perhaps another attorney can enlighten us both. The only thing I know to do is keep the points off your record, but the offense will still show up.
One thing I can tell you, and everyone else reading this question, is that writing letters to judges is rarely, if ever, an effective strategy. I can't stand it when my clients fire off letters to judges without running it by me, because it usually makes matters worse. Judges rarely read the letters anyway, they just copy them and provide it to the State Attorney.
The only way to get it removed is to file a motion to set aside disposition and then we set it for a hearing and hope the officer does not show or you have a legal basis to win the ticket. I do not know if a Judge would even consider the motion this long after. You would have to have a really good reason that you need it off your record.