Any owner of real estate, or of a subdivisional part thereof, on which there is stagnant water, who may have commenced and done a portion of the work before the time of receiving bids shall have expired, shall have the right to do the work to completion of his or her own portion thereof, upon giving bond, with two or more sureties, in a sum to be fixed by the city council, should he or she, at any time prior to the last day for receiving bids, notify the city council, in writing, of his or her intention to do so. The bond must be filed within five days after the amount shall be fixed by the council and must be approved by the mayor. (Prior code § 21.04.021)