What is the cheapest way of depositing/transferring small-ish (~US$500-1000) amounts of cash (RMB) into a US bank account? I will have to do this multiple times and I'd prefer not to wait and combine them into one big wire transfer.

I have a Bank of America checking account and I know that I can take money out without charge at ATMs of China Construction Bank. Can I deposit money there?

I can open a new bank account if there is a US bank that's convenient for this purpose.

Thanks!