Bessant, who has led the bank's tech division since 2010, was asked by CNBC's Deirdre Bosa what her reaction was to Apple's announcement on Monday. Keep in mind that Bank of America, the second biggest U.S. lender by assets, is a financial giant with relationships with 66 million consumers and small businesses.
"My reaction when I saw the announcement was, first competitively, all of the features that are in that card are offerings we have today," Bessant said on "Squawk Alley." "The card plastic for swiping itself, all the way through to the mobile and electronic wallet."
Bessant joins some other industry voices, including analysts at Goldman Sachs, to downplay the innovation that Apple CEO Tim Cook boasted about on Monday. Goldman did so even though it is the bank partner for the Apple Card. The new service relies on Apple Pay for mobile payments and includes a titanium card for situations where Apple Pay isn't yet accepted.
When asked if the Apple Card would at least widen the pool of card users by signing up millennials, Bessant allowed that her bank would be closely watching how the new product performs.
"We see new cards in the marketplace all the time," Bessant said. "I think it's an interesting announcement. We'll pay a lot of attention to it."