This was a CIA/Joint Chiefs of Staff operation, so was under the control of the Executive branch, but was long enough in the planning (going back to the Eisenhower administration) to have been shared to some extent both officially and unofficially with congress.
According to Jim Rasenberger's book The Brilliant Disaster: JFK, Castro, and America's Doomed invasion of the Bay of Pigs, p. 150 "[Alan] Dulles and [Charles] Cabell [Director and Deputy Director of the CIA] had been keeping Congress vaguely informed of the plan in intelligence briefings." Rasenberger notes that chairman of the Senate Foreign Relations Committee J. William Fulbright knew enough about the planned invasion to use a shared ride with the President on Air Force One to counsel strongly against the plan (pp. 151-152).
See also: Bay of Pigs declassified : the secret CIA report on the invasion of Cuba
and
Bay of Pigs : the untold story
