Will they come to my home to arrest me on a bench warrant for a misdemeanor?

Depends. In Utah it depends on the jurisdiction. For example, in St. George, a relatively small town, the police will come and arrest you on a bench warrant. They usally like to do this on a Friday so you sit in jail until monday. In Salt Lake City you could go years without any problems.

That said, you should call the court and find out when you can come in and see the judge. Or, you could retain an attorney to file a motion to recall the warrant. Either way, you will get a new court date to appear.

Hope this helps.