When it is necessary for any county officer or his or her deputy or assistants, except any county sheriff or his or her deputy, to travel on business of the county, he or she shall be allowed mileage at the rate per mile allowed by section 81-1176 for travel by personal automobile upon the presentation of his or her bill for the same accompanied by a proper voucher to the county board of his or her county in like manner as is provided for all other claims against the county, but if travel by rental vehicle or commercial or charter means is economical and practical, then he or she shall be allowed only the actual cost of the rental vehicle or commercial or charter means. The county board may establish different mileage rates based on whether the personal automobile usage is at the convenience of the county or at the convenience of the county officer or his or her deputy or assistant.