a place near the Bund, Shanghai where we can deposit our luggages while we tour around the area?

Well, you can deposit our luggages at big supermarkets nearby the Bund, such as TESCO. The nearer branch is located at No.545, East Jinling Road, Huangpu District. It's about one mile (1.5 kilometers) away from East Nanjing Road. You can put your luggage there. :-)

Hi again, will our luggages be safe to deposit at those large supermarkets? Do you have any idea how much is the deposit fee?

Well, generally speaking your luggage will be safe. But it is not advised to leave valuables and important documents like passport there. BTW, the service is available at the Customer Center of the supermarkets. After depositing, the staff will give you a small metal or plastic card or something else. Keep it well for it will be used to get your luggage back.

Most supermarkets offer the service for free. No worry.