Again I feel that you too have confused JFK with Allan Dulles. It was the height of the cold war and the CIA did things pretty independently, while JFK would have to do cartwheels and headstands in Congress to get any of them approved. Was it not JFK who said the "CIA would be splintered into 1000 pieces"? True, those covert (and anti-communist) actions did take place while he was in office.
Lynch L. Grayston, Decision for Disaster: Betrayal at the Bay of Pigs
What I get out of these and other sources I've read is that the operation was undermined not so much by JFK himself as by some of the advisors he relied on, especially Dean Rusk, who represented the policies of the Dulles brothers' old opponent Dean Acheson. Acheson, Paul Nitze, Maxwell Taylor, and others aligned with them had been opposing J.F. Dulles' foreign policy during the Eisenhower administration and gained influence with JFK's election. They scapegoated Dulles for their own undermining of the Bay of Pigs in order to promote their own foreign policy agenda, IMO.