I find it interesting that a bicycle ticket can be tied into a drivers {?} license suspension. Unless you meant a motorcycle ? motorbike ?
Assuming it was a pedal powered bicycle, i'll guess you were in your own county, or the next one over , from your home. Maybe next time instead of trying for 2 weeks to pay online -- just make a trip in person to the county offices and pay the nice lady/man behind the counter and get a receipt. That is why they have these staff positions filled.
Sometimes trying the "easy + cheap" way to take care of an issue [ internet payment ] , comes out more expensive. Sure, the ticket should have been entered into the computer system, but it wasn't, and an in person visit - where you bring the paper ticket , pay with physical money, and get a paper reciept , is virtually foolproof.