According to your query you did not fail to appear. Further, you state that you have documents that show you resolved the matter before the bench warrant was issued. That being the case there shouldn't be any penalty however people spend time in jail when they get arrested on an outstanding warrant and have to wait to get the matter set down before a judge. It would be appropriate to file a motion to set aside the bench warrant and get the case before a judge as soon as possible. Otherwise you may get a traffic ticket, the cop runs your name on the mobile computer terminal in the patrol vehicle and the warrant pops up, in which case you get arrested.
Which judge where you supposed to appear before. All of the judges in the the circuit for Hart County (Hodges, Bailey, Malcolm) are reasonable people in my experience. Call the correct judges office and offer to fax the info to them and see where that gets you.