This seems like a very easy problem to fix: go pay your fine before travelling, and the bench warrant should go away.

Warrants can't always just be paid off. I had a Probation Violation
in Florida for A DUI and even though the stop by the cop before the ID check was totally illegal (pretextual) they extradited me next to hardcore felons in a dirty old van around 3 AM to the other county. (Maybe an attorney knows: Whatever happened to "fruit of the poison tree"?) We offered to throw a large sum of money at them to clear it up (so I didn't lose my job in another state) but they wouldn't have it. Ended up doing a month for something (1st offense DUI) that would normally have gotten me at most 1 day in jail. Weird.