Hi Corylea. Hydra14 is absolutely right (thank you Hydra14!), the mayor does not have to empty the trash bins.

If you decide you want to move any of the trash bins (or other upgrade item you've placed in the town) just hold your finger on it for 3-5 seconds to enter placement mode, then move it to where you'd like it and confirm the new location. The demolition order would be used for a town upgrade that you want removed from your town and not have it placed in your mayor's pockets. I hope this helps!