There are numerous services with names like Money2India, Remit2India, Xoom, etc that are offered by Indian banks and other agencies which will take money out of your US checking account and deposit the Indian rupee equivalent into your NRE/NRO account.
It takes a day or two to set up the service, and then anywhere from one day to one week to make a transfer (depending on how much service charge you are willing to pay for the transaction. It is not necessary to have an account with the Indian bank offering this service. Indeed, I am surprised that your own Indian bank where you have your NRE/NRO account does not offer this service.