The BoA logo on the payment options page is confusing. In this case, you are making payments to an account which is with BoA - so, it is not paying using BoA. If you have any bank account in India with online banking facility, you can do a 'Funds Transfer'. One of the categories of funds transfer is NEFT.
I paid my fee using ICICI bank - all I have to do was to use the unique beneficiary number & IFSC code given by the ustraveldocs website. If you are using ICICI, note that you either have to initiate the transfer as per Indian working hours or schedule it to initiate transfer during Indian bank working hours (Here, I don't understand their definition of online banking ). It took few hours for the ustraveldocs website to recognize my payment, but it was much easier than asking someone in India to go to a bank and pay the fee for you.
Hope this helps. I looked for this information everywhere, no one explained this to me... I had to figure it out. Came back to post this as it may help others like me...