Will a bench warrant go away after paying late on speeding ticket?

It would be appropriate to file something with the court that issued the bench warrant asking that the bench warrant be quashed, and attach a receipt showing payment.  If it is no0t quashed, a quick court appearance likely will resolve the matter. Most courts have a day and time for people to appear on bench warrants to get the case reset on the court docket.  Also, be aware that an 'unpaid ticket' will suspend your drivers license until the matter is resolved so getting the case in court resolved (i.e. bench warrant removed) is important so the DMV record ends up being accurate and you don't get arrested on the warrant or for driving while suspended.