Four will guarantee a kill on an incoming Barracuda, six will put paid to a White Shark, and eight to a Killer Whale. So, I'm leaning to at least eight AMS in a single bay. But should a Clan WarShip (pre-Jihad/Reaving) mount more? If so, how many more?
Actually the numbers are 4, 7, and 11 for Barracudas, White Sharks, and Killer Whales, respectively - at least for a single bay. Each AMS does 0.3 capital scale damage (bay rounded up), and needs to do as much damage to the capital missile that the missile can do to the target, so Barracuda 2, White Shark 3, Killer Whale 4. So 4 does 1.2 damage (rounded to 2) to kill a barracuda, 7 do 2.1 (rounded to 3) for a White Shark, and 11 do 3.3 (rounded to 4) for a Killer Whale. Now if you are super rules-lawyering muchkinny, then you could just put 4 bays of single AMS to counter all non-Kraken capital missiles - and only mount them on the broadsides, fore and aft for total coverage.
I personally tend to put between 3 and 5 AMS in a single bay per firing arc, but have gone up to 7 on rare occasions. Generally speaking, this makes most of my warships "immune" to barracudas, while also providing a penalty to other's attack rolls.
My thoughts on this are mostly that the biggest threat to any warship is going to be capital missiles, likely with nukes on board. The Amaris rebellion showed this to an extent and if we decide to take reality into things, then doctrine is often based on the last major war. Naval forces were barely used in operation Klondike, so the last real war they were involved in (as far as the clans are concerned) is going to be the Amaris Coup. So lessons learned during that war are going to be applied to new warships.
There are one really big take away from the conflict, that warships are exceeding vulnerable to capital missiles of any sort. This leads to two solutions, which I tend to include in my warships. The first is the inclusion of AMS, and what I make to be enough to make it difficult for opposing missiles to hit the ship (in reality its not that great of a difference though). The second is to include enough ASF to function as a local control force - only carriers should have enough fighters to properly use them offensively. These ASF would be used to counter bombing runs by other aerospace fighters and to do their best at knocking out capital missiles targeting friendly warships. My thoughts on using both are that if you rely on one thing then whatever beats that one thing has free reign on targeting your warships.