This video checks out some different tactics for ASW. At the end of the day, just use airplanes. Unless you're the sub...then go deep or in the layer and slow.
Times:
0:009:32 Checking units in the database, general overview
9:3311:12 Tactical Considerations
11:1322:19 Setting up regular missions
22:1925:41 Setting up convoy escort
25:4230:04 Setting up Maritime Patrol Missions
30:0535:29 First sub kill
35:3039:22 Send in the bears (tu142)
39:2244:55 Second sub kill
44:5649:32 Change of strategy (Bring units in a tighter area)
49:32End Conclusions, seeing how many we missed.

Losses/Expeditures:
1x APR2 OrlanM
18x RBU6000 Salvo [12 rnds]
75x RGB1 [NATO BM1, Search, Passive Omni]
160x RGB15 [Refined Search, Passive Omni]
60x RGB25 [Track, Passive Directional]
86x RGB55A [Track, Active/Passive]
165x RGB75 [Basic Search, Passive Omni]
2x SET40M [MGT2]