As it happens, the QuickPay and SurePay services are actually one and the same. They are part of the P2P transfer service called clearXchange that ethelbert mentioned. The banks just call them by different names. clearXchange can work with any U.S. bank, but member banks (which include, Chase, Wells Fargo, Capital One, Bank of America, FirstBank and US Bank) make setup easier.
Since both the sending and receiving accounts Pauly01 wanted to transfer between are clearXchange member banks (Bank of America and Wells Fargo), she could skip registering at clearXchange.com and just log into bankofamerica.com, go to “Transfers” - “Send Money to Someone” - “Using their email address or mobile number”, and enter the email address or mobile number associated with the receiving Wells Fargo account.
If the sending and receiving accounts are owned by different people, I personally prefer the above method to sharing account numbers.