ASW Air Missions are very valuable. Investing in both the squadrons and pilots will give you good returns.
I play Allied against the AI. In my current game, I'm up to January 1943. About once a month I will do an intel check by opening up both sides (yes, I confess that's terribly close to cheating.... but heck, I'm investing up to four years in one entertainment category, I'm allowed....I am more of a Historian and just can't bear not knowing what is happening to the other side.. ) After a year of war most of the Japanese Subs that were actually destroyed were from Mines at major ports (Sydney, Columbo, Pearl). Seems the AI likes to launch midget sub attacks.
The next major killer of enemy subs were 250 pound bombs hits from my ASW Air Patrols. During your combat resolution phase you will see Airgroup contact and attack reports against enemy submarines and surface targets. Mostly these are inaccurate reports from over-eager pilots.... but a real percentage are actual hits that, even if they don't sink the sub, will force it to return to base for repairs.
For the Commonwealth Countries (British, Australia and New Zealand) the Hudson IIIa is an excellent ASW aircraft. It's one of the first allied bombers equipped with radar. It's really too light of an aircraft to risk for ground attack missions. With good range and some bombs, I've come to rely on it for ASW coverage.
It takes about six months of training to bring your aircrews up to the skill level to make a difference. I will mix their mission levels (say 40% ASW - 40% Training - 20 % Rest). Yes, if you work them at 80% training, they will learn up faster,,,, but in the early days of the war I need Missions flown. Once they get up to the 70% ASW skill level, you can reduce training and concentrate on ASW.
The ASW Skill set will include search levels (against subs). I still like to mix my training for search and ASW squadrons. I use the Kingfisher squadrons to train up ASW and Search Pilots (other threads mention these as great training groups for all your naval air crews).
Note: Not really part of your thread, but I was really surprised at the number of Jap Fleet boats destroyed by Mines (not just the midgets). It's easy to get lost in all the layers of details in this game, but you want to look at Mine Warfare as an ASW defense for your major ports.
Welcome back from 'over there'. We all appreciate your efforts.
Fair Winds and Following Seas