All moving of trees upon any public place in the City made necessary by the moving of a building or structure, or any other private enterprise, shall be done under the supervision of, and with a permit from the City Arborist, and at the expense of the applicant or person seeking the removal of such tree. Such applicant, as one of the conditions of obtaining a permit, shall deposit with the City such sum in cash as the City Arborist may determine and specify to cover all of the cost of moving and replacing such tree, if the conditions of such permission require the replacement thereof. However, in lieu of such cash deposit, the City Arborist may, in his discretion, accept a good and sufficient bond in like amount conditioned upon the payment of all the cost of such moving and replacing.