You may want to try a service called CheckFree. I have used their bill-payment service for over 10 years, with never one error on their part. Deposits are posted overnight. Some payments go out the day they are entered. They provide online access to my check register, savings account, and MasterCard account.
All transactions are as of the last business day.
Transfers between accounts is a valuable capability. I recognize that history may not always repeat itself, but nonetheless stocks have historically fared better than bonds during these holding periods. I don't for three reasons. First, I don't think stocks in the next 15 years will return a lot more than bonds. You can find a related topic discussed in a recent essay by William Bernstein of Efficient Frontier Advisors, who walked me through his persuasive thinking on this point.