Call the prosecuting atty. (or better yet, write)
Advise that you are busy and would like to appear tocontst it, but you don't know if you can. Advise him that you'd be willing to pay a fine, but you feel as though you are not guilty of the stated offense, but you;d entertain pleading guilty to something else.
Your fine won't drop, but you'll probably get offered something that is fewer points.