You don't want to engage airplanes, even if you have the best the Navy Department has to offer you for gunners and spotters. The planes "fone home" and will report your position, and the Bear might be on the alert even more, zigging at the most inopportune time. A CV group will "spawn" CAP for itself, and if a fishing boat spots you, and you are within the planes' operating radius, they will send some your way, continually. Not seen, not detected, you might see nothing until sound reports "Warships! Closing!..."
Another thing to do is to keep moving when on the surface, even if only in circles, so that your dive times are reduced. In the FotRSU mod, we have found issues with the airplanes. We have not looked at the Stock game files, but would not be surprised to find similar issues, but what happens in FotRSU, is that if an airplane is not properly configured in all aspects of its weaponry and sensors, then they will often not attack, and conversely, your crew does not attack them either. Very strange behavior, but it did happen in FotRSU until s7rikeback fixed it...
