In all cases where the estimated cost of the work to be done at any one time under the direction of the commissioners shall exceed five hundred dollars [($500)], the same shall be let to the lowest responsible bidder, and the commissioners shall advertise for sealed bids, by notice published in some newspaper published in the county in which the petition is filed, and may advertise in one or more newspapers published elsewhere. If there be no newspaper published in the county in which the petition is filed, they shall advertise in some newspaper of general circulation in the district, which said notice shall particularly set forth the time and place when and where the bids advertised for will be opened, the kind of work to be let and the terms of payment. Said commissioners may continue the letting from time to time, if in their judgment the same shall be necessary, and shall reserve the right to reject any and all bids.