I was a US Navy ASW tech in the '70s, and hunting nuke subs is more complicated because they can dive deeper and stay forever. ASW in WWII was simpler in one way - get a sub contact, stick a pin in the chart and draw a 100 mile radius circle around it. He HAS to come up somewhere within that circle in the next 48 hours. When he does, drive him under again, mark the chart and draw another circle - repeat until he runs out of amps.
ASW ran thru a whole bunch of changes during WWII. At the beginning the Brits were so short of escorts they would send out anything that could carry a couple of depth charges and a Lewis gun, so the few escorts available for convoys had an SOP to attack, but quickly break off and return so as not to leave the convoy unguarded. That policy gradually changed as more escorts became available, and some escorts that sailed with a convoy were detailed to stay with the contact until it was sunk, while the rest went on with the convoy. ASW became more and more aggressive as resources became available, and when escort carriers like the USS Guadalcanal started coming off the slips in larger quantities, those not needed for actual escort were organized into hunter-killer groups whose only task was (like the name implies!) to find and destroy U-boats.
So the later war period this would be realistic, when more subkillers became available the whole philosophy changed from a defensive posture to an offensive extermination. If you can find a copy read "The Cruel Sea", an excellent encapsulation of ASW in WWII.