I have added ALL our CC bills (except 2, which are not on BBPS) and other bills (electricity...) to HDFC's AutoPay feature in my SBMax SB account with HDFC Bank. For the last 3 years, they are fetching all those bills and paying them before 4 days of their respective due dates. So far, so good.
Only on 2 occasions, that auto feature failed n money debited came back. HDFC sends intimations of such rare failures (due to recieving bank's failures) about 3 days before the due dates n asks you to pay manually.
I use the same account/DC to pay such bills - so that all payments are in one place.
HDFC is good at doing this dirty work for me. And, I let them do it. Ha ha ha